The correct option is D Did / live
The simple past tense is used to indicate or describe something that happened or existed in the past. It can be used to refer or describe an action that has been completed and there is no time mentioned. However, in interrogative sentences, the only difference between a question in the present tense and a question in the past tense is the change in the auxiliary verb. So, the base form of the verb remains the same and the auxiliary becomes the past "did". Hence, C is correct.
A, B and C are incorrect as the main verb in a question remains the same. Hence, the use of "lived"renders them incorrect.