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I need you to be more specific in your question(s) if you could. When we answer general ones like what happens if...", "what are my rights", or "what are my options", we have to give general answers and, invariably, the customer responds with "I already knew that". This type of forum works better if you ask specific questions so we know exactly what you are looking for.
I'm not sure what you mean by "invoking the lease" but a landlord can sue a tenant for "holdover" or for not paying the rent under a breach of contract theory. The statute of limitations varies form state to state but if you will tell me what state you are in I can find it for you.