Is paying rent late cause for breaking lease

It can be, normally most standard leases allow for eviction if the renter is normally or usually late

It depends on (1) what is written in the lease and (2) the laws in your location. Tell us where you are and we can give you a better answer.

Are you the landlord or the tenant? Who is trying to break the lease?

I am having difficulty making sense out of your question. Are you asking if the LL can evict a tenant for paying late, if so then very , very often a big yes.

A lease has terms. Both the tenant and the landlord are required to abide by those terms. Any violation of those terms can be grounds for terminating the lease.

Paying rent is one of the terms of a lease. The remedy, for the landlord, is to serve a notice to vacate, followed by the request for an eviction order in the courts.