The charging of late fees is illegal under most residential leases EXCEPT when the fees reflect the actual loss to the landlord and that amount has been agreed upon in advance by you. The fact that you agreed to pay more than the actual loss is of no moment. Your landlord cannot contract around the law.
ALSO, your landlord cannot charge you attorneys' fees. While your lease might say that a "prevailing party" is entitled to obtain attorneys' fees, your landlord has not be adjudicated to be the prevailing party in any lawsuit.
Your landlord can only evict you for non-payment of rent, not for non-payment of attorneys' fees and late fees. Here's the upshot--they might sue you for unlawful detainer anyway, and unless you are represented by experienced unlawful detainer defense counsel, the Judge might accept the landlord's calculation of "rent" due.
The safest course is to pay the landlord what he wants and then sue him in small claims court for the return of the fees.