@Allison Panila,
What you see here is the difference between "Good LLs" and "Bad LLs".
As @Russell Brazil stated, the basement unit is illegal to begin with. So therefore anything that comes out of a contract concerning the basement unit isn't enforceable in the court of law. Think for instance you go to your local drug dealer and sign a contract for 3 kilos of Cocaine at $50k a kilo and when it comes time to pick up your product he is selling for $55k. If you then take the dealer to court the judge is going dismiss because you contracted for an illegal service. (This is an extreme case I know but the logic applies).
So your original question of "can a LL change the contract", in this case yes he can. Simple because in a court of law the contract holds no weight due to it being an illegal service to begin with.
So the scorched earth response Jim K said he would do it not only impossible in this situation, but also illegal if he actually succeeded in get an 'eviction' on her record. And with all due respect to Jim K there is really no reason to imply insult the Highway State, assume she is entitled or to basically be a dick behind the keyboard. Allison has come here asking a legit, legal question and you seem to be taking out some personal issues on them.
Now if we can get into theory craft of your question as to if the LL can change the contract, usually that is a no. But then the question come down to the undefined wording of "three times". Generally accepted contract (look at the lease people sign daily with apartments) "three times" means overnight stays. One would also argue the term is too vague to be properly interpreted in a legal sense. Does the pizza delivery guy dropping off dinner count as a visitor? What about the UPS guy who is delivering school books from amazon? If her car pool driver needs to use the bathroom before heading to school does that count? How about someone coming over to pick up a book needed to study? What about 3 students that come over to do a study session, does each person count as a 1 time visitor or the the group as a whole counted as 1 time? What if the BF comes over Friday morning and doesn't leave until Monday Morning, is that just 1 time? You can see where this is going I assume.
Reasonably I would assume (see the word assume and know that it makes an *** out of u and me) that any judge or arbitration would side on the fact that "three times" would refer to three individual times spending the night.
Reality is the contract is poorly written, or perhaps you have not given enough detail since you didn't want to get into the weeds here, and is illegal given the way it is written.
That said she should just pay the $50 and tell the guy to shove it, not worth the hassle.