Do insurance companies drop/cancel your policy if youhave a lawsuit(premise liability) or demand letter and you havent report it to them? What are some reasons of why a insurance will drop you? Im talking about Home Insurance.

The best source to research WHY your company can choose to non-renew you (besides non-payment): Your Policy! The policy will outline ALL reasons you can be dropped:
Typical reasons:
Underwriting violations
misrepresentation
claims history
insurer leaving market

Having a pending lawsuit would not be a reason unless it's pending due to misrepresentation or underwriting violations.