He can evict you on late payment. Obviously, the late fee will exist only when you are late in payment. Even if you are late, you still have chance after eviction notice to pay the rent in full and stay in the house. Your landlord can't evict you like this.
Technically he can but if he has any decency he will give you a chance to pay them and give you a second chance. And as was said, once you get the notice you still have a chance to pay the fee.