Apex class - 

public with sharing class InvoiceLineTriggerHandler {

    public class InvoiceLineSchedule {
        public Date lineSvcStartDate {get; set;}
        public Date invcLineSvcDeliveryDate {get; set;}
        public String invcScheduleType {get; set;}
    }
    
    public static void runtrigger(List<kugo2p__KugamonInvoiceLine__c> newList, List<kugo2p__KugamonInvoiceLine__c> oldList, Map<id,kugo2p__KugamonInvoiceLine__c> newMap, Map<id,kugo2p__KugamonInvoiceLine__c> oldMap)
    {    
        if(trigger.isAfter && trigger.isInsert) {
            afterInsert(newList,newMap);
        }
    }
    
    private static void afterInsert(List<kugo2p__KugamonInvoiceLine__c> newList, Map<Id,kugo2p__KugamonInvoiceLine__c> newMap) {
        // Update the Service terms on the Invoice level
        updateInvoiceServiceDates (newList, newMap);
    }

    private static void updateInvoiceServiceDates (List<kugo2p__KugamonInvoiceLine__c> newList, Map<Id,kugo2p__KugamonInvoiceLine__c> newMap) {
        Set<Id> invcIds = new Set <Id> ();
        Map<Id,InvoiceLineSchedule> invcScheduleMap = new Map<Id,InvoiceLineSchedule> ();

        for (kugo2p__KugamonInvoiceLine__c eachInvoiceLine: newList) {
            invcIds.add (eachInvoiceLine.kugo2p__Invoice__c);
        }

        List <kugo2p__KugamonInvoiceLine__c> ivcLines = [Select id, kugo2p__Invoice__c , kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceDelivered__c, kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceStart__c, kugo2p__SalesOrder__r.kugo2p__BillingFrequency__c, kugo2p__SalesOrder__r.kugo2p__InvoiceSchedule__c from kugo2p__KugamonInvoiceLine__c Where kugo2p__Invoice__c in :invcIds WITH SECURITY_ENFORCED];

        for(kugo2p__KugamonInvoiceLine__c eachInvcLine:ivcLines){

            InvoiceLineSchedule invcSchedule; 
                system.debug('Nandita>>>>>>>>>>>>>>>>>>>>>>'+invcSchedule);
            if (invcScheduleMap.containsKey(eachInvcLine.kugo2p__Invoice__c)) {
                 
            
                invcSchedule = invcScheduleMap.get(eachInvcLine.kugo2p__Invoice__c);

                if (eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceStart__c < invcSchedule.lineSvcStartDate) {
                    invcSchedule.lineSvcStartDate = eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceStart__c;
                }

                if (eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceDelivered__c > invcSchedule.invcLineSvcDeliveryDate) {
                    invcSchedule.invcLineSvcDeliveryDate = eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceDelivered__c;
                }
            } else {
                invcSchedule = new InvoiceLineSchedule ();
                invcSchedule.lineSvcStartDate = eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceStart__c;
                invcSchedule.invcLineSvcDeliveryDate = eachInvcLine.kugo2p__ServiceDeliverySchedule__r.kugo2p__DateServiceDelivered__c;
                invcSchedule.invcScheduleType = eachInvcLine.kugo2p__SalesOrder__r.kugo2p__InvoiceSchedule__c;
                invcScheduleMap.put (eachInvcLine.kugo2p__Invoice__c, invcSchedule);
            }
        }

        List <kugo2p__KugamonInvoice__c> invcList = [Select id, Service_Start_Date__c, Service_End_Date__c from kugo2p__KugamonInvoice__c where id in :invcIds WITH SECURITY_ENFORCED];

        List <kugo2p__KugamonInvoice__c> invcListUpdate = new List <kugo2p__KugamonInvoice__c> ();

        for (kugo2p__KugamonInvoice__c eachInvoice : invcList) {
            if (invcScheduleMap.containsKey (eachInvoice.id)) {
                eachInvoice.Service_Start_Date__c = invcScheduleMap.get (eachInvoice.id).lineSvcStartDate;
                eachInvoice.Service_End_Date__c = invcScheduleMap.get (eachInvoice.id).invcLineSvcDeliveryDate;
                invcListUpdate.add (eachInvoice);
            }
        }

        if ( !invcListUpdate.isEmpty () ) {
            // Database.update(invcListUpdate); // Moved to Future Method
            updateInvoices(JSON.serialize(invcListUpdate));
        }  
    }

    @future
    private static void updateInvoices(String invoiceList){
        List<kugo2p__KugamonInvoice__c> lstInvoices = (List<kugo2p__KugamonInvoice__c>)JSON.deserialize(invoiceList, List<kugo2p__KugamonInvoice__c>.class);
        Database.update(lstInvoices);
    } 
}

Test Class:

@isTest
private class InvoiceLineTriggerHandlerTest {
    @isTest
    static void customDataCreateForInvoiceLineTrigger(){
        List <Trigger_Execution__c> triggerExecList = new List <Trigger_Execution__c> ();
         Trigger_Execution__c invoiceLineTriggerCustomSetting = new Trigger_Execution__c (Name = 'InvoiceLineTrigger', is_Execute__c = true);
         Trigger_Execution__c invoiceTriggerCustomSetting = new Trigger_Execution__c (Name = 'InvoiceTrigger', is_Execute__c = true);
         Trigger_Execution__c orderTriggerCustomSetting = new Trigger_Execution__c (Name = 'OrderTrigger', is_Execute__c = true);
        triggerExecList.Add (invoiceLineTriggerCustomSetting);
        triggerExecList.Add (invoiceTriggerCustomSetting);
        triggerExecList.Add (orderTriggerCustomSetting);         
        insert triggerExecList; 
    }

    @isTest
    static void test1() {
       // try{
            customDataCreateForInvoiceLineTrigger();
            Test.startTest();
            //account
            Account testAccount = TestKugamonDataFactory.createAccount();
            Insert testAccount;
            
            //contact
            Contact testContact = TestKugamonDataFactory.createContact(testAccount);
            Insert testContact;
            
            //custom pricebook
            Pricebook2 testCustomPriceBook = TestKugamonDataFactory.createCustomPriceBook();
            Insert testCustomPriceBook;
            
            //kugamon settings
            kugo2p__KugamonSetting__c kugamonSettings = TestKugamonDataFactory.createKugamonSettings(testCustomPriceBook, new kugo2p__Warehouse__c());
            Insert kugamonSettings;
            
            //warehouse
            kugo2p__Warehouse__c testWarehouse = TestKugamonDataFactory.createWarehouse(kugamonSettings);
            Insert testWarehouse;
            
            //additional account info
            kugo2p__AdditionalAccountDetail__c additionalAccountInfo = TestKugamonDataFactory.createAdditionalAccountInfo(testAccount, testWarehouse);
            //insert additionalAccountInfo;
            
            //product
            List<Product2> lstProducts = TestKugamonDataFactory.createProducts();
            Insert lstProducts;

            //Additional Product detail
            kugo2p__AdditionalProductDetail__c apds = new kugo2p__AdditionalProductDetail__c(Name='PROMO 1 Year End User 5,000-9,999 Employees', kugo2p__ProductDescription__c = 'SecureSuite Membership End User 5,000-9,999 Employees',
            kugo2p__ProductFamily__c = 'SecureSuite', kugo2p__ReferenceProduct__c = lstProducts[0].Id, kugo2p__Service__c = true, 
            kugo2p__StandardPrice__c = 10978, kugo2p__UnitCost__c = null, kugo2p__Active__c = true, kugo2p__PrintProductTextandTerms__c = true, 
            kugo2p__KitBundle__c = true, kugo2p__KitBundlePricing__c = 'Member Prices Only', kugo2p__UnitofTerm__c = 'Year', kugo2p__ProductCode__c = 'CIS-SSM-SLTT');
            
            
            //Create Pricebook Entries
            list<PricebookEntry> lstPricebookEntry = TestKugamonDataFactory.createPricebookEntries(lstProducts, Test.getStandardPricebookId(), testCustomPriceBook);
            Insert lstPricebookEntry;
            
            List<kugo2p__TaxLocation__c> lstTaxLocations = TestKugamonDataFactory.createTaxLocation(testAccount, additionalAccountInfo, kugamonSettings);
            Insert lstTaxLocations;
            
            id RecordType1=[SELECT Id,DeveloperName  FROM RecordType WHERE sObjectType = 'Opportunity' AND Name = 'New'].id;
            
            //opportunity
            Opportunity testOpportunity = TestKugamonDataFactory.createOpportunity(testAccount, testCustomPriceBook, 'Closed/Won');
            testOpportunity.kugo2p__SyncSource__c = 'Primary Order';
            testOpportunity.RecordTypeId=RecordType1;
            Insert testOpportunity;
            
            //Create Opportunity Line Items
            list<OpportunityLineItem> lstOpportunityLineItems = TestKugamonDataFactory.createOpportunityLineItems(testOpportunity, lstPricebookEntry);
            Insert lstOpportunityLineItems;
            
            //order
            id RecordType=[SELECT Id,DeveloperName  FROM RecordType WHERE sObjectType = 'kugo2p__SalesOrder__c' AND Name = 'New'].id;
            kugo2p__SalesOrder__c testSalesOrder = TestKugamonDataFactory.createSalesOrder(testAccount, testContact, testOpportunity, testCustomPriceBook, testWarehouse);
            testSalesOrder.RecordTypeId=RecordType;
            Insert testSalesOrder;
            
            //invoice
            List<kugo2p__KugamonInvoice__c> testInvoice = TestKugamonDataFactory.createInvoices(testAccount, testSalesOrder);
            testInvoice[0].kugo2p__InvoiceDueDate__c = system.today().addMonths(6);
            Insert testInvoice;
            kugo2p__KugamonInvoice__c testInvoice2=[Select id, Opportunity_Record_Type__c, Date_Difference__c     from kugo2p__KugamonInvoice__c where Id=: testInvoice[0].id];
            system.debug('Date difference1-'+testInvoice2.Date_Difference__c);
            
            //invoice lines
            List<kugo2p__KugamonInvoiceLine__c> invcLines = TestKugamonDataFactory.createInvliceLines(testSalesOrder,apds,testInvoice[0]);
            Insert invcLines;
            //system.debug('invoiceLines '+invcLines);
            Test.stopTest();
       /* }catch(DmlException e){
            System.debug('A DML exception has occurred: ' +
                         e.getMessage());
        }  */       
        
        
    }
}