What is the maximun a landlord can charge for a late fee?

There is neither a requirement or prohibition for charging late fees or a statutory maximum. The only statutory issues is that late fees need to be defined in the lease.

Courts, however, can rule against an unreasonable charge, but no guidelines are given about what is unreasonable.

Also keep in mind the LL does have to even accept your late rent, he can evict. What is your rent and what was charged for being late, how late?