The correct options are
A lived
B lived the life of a warrior
Options A and B are correct. Option A is correct as the verb lived is an intransitive verb. Although it does tell where, how or when David lived, it tells that he was alive. Option B is correct as it gives information about how David lived. He lived a life of a warrior. Option C is incorrect the preposition'to' is unnecessary. Option D is incorrect as the preposition 'at' is unnecessary. Hence options A and B are correct.