You are not able to pass other object values directly into a trigger but you are able to query for additional information in a trigger. That being said, you need to be careful when querying from inside a trigger because you are limited to 100 Queries and if you include a trigger in a for loop you can kill your process rather quickly. I will provide two links at the end of this response that explain governor limits and trigger practices a bit more. To answer your question though you would do something like this.

set<String> businesses = new set<String>();
for(Case c : trigger.new) {
    businesses.add(c.business);
}

list<ProductLine> productLines = [SELECT id,Business FROM ProductLine WHERe Business in :businesses];
map<String,ProductLine> productLineMap = new map<String,ProductLine>();
for(ProductLine pl : productLines){
     productLineMap.put(pl.Business,pl);
}

for(Case c : trigger.new) {
    c.productline = productLineMap.get(c.business);
}

This assumes that each business is associated to only one productline. Some adjustments would be made if you needed to bring back multiple product lines for a single business. If you need more help just let me know. Also, providing some more code might help.