What is wrong with using this sentence in a business letter? lots of liberty students like to go to pop's and think it is really cool.

There’s no correct grammar in this sentence if your question is telling you to pick the correct sentence it would be

“A lot of Liberty students likes to go to Pop’s and thinks it is very cool”

I think that the problem is that it uses informal language making it feel unprofessional. Remember that informal language is used when you want to be casual, in a conversation with friends or family members. It has a personal tone.

Here, formal language must be used as it serves to academic or professional purposes. It doesn't use colloquialisms, contractions, or first person pronouns. Formal language tries to used specialized words that give the text it a tidy and neat appeareance.

A way to rewrite this sentece could be:

Numerous Liberty students have preference for going to Pop's (has contraction because it is a proper noun) because they think it is a nice place.

can you take a picture of the passage so i can answer your question