The correct answer is C. Live.

1. Live: This option is correct because it is the base form of the verb, which is appropriate after the auxiliary verb "does." In English, when using "does" (which is a third-person singular form), the main verb should be in its base form.

2. Lives: This option is incorrect because "lives" is the third-person singular form of the verb, used with "doesn't" (does not) in negative sentences or questions. Since "does" is already the third-person singular auxiliary, the main verb should be in its base form.

3. Lived: This option is incorrect because "lived" is the past tense form of the verb, which does not fit the present tense question structure with "does."

4. Living: This option is incorrect because "living" is the present participle form, which is not used with "does" in a question about habitual actions.

Summary:

- C. Live is the correct choice because it matches the grammatical structure required after "does" in a question about present habitual actions.