Revised - Tim added an excellent point. --- In some situations, the speaker can treat the recent past as the present and the grammar changes accordingly. version 1a - Last summer, I saw my friend Joe for the first time in a few years. He didn't mention where he lived (or was living). Grammatically correct. All verbs backshifted. "Where he lived" refers only to the moment of the conversation (last summer). version 1b - Last week, I saw my friend Joe for the first time in a few years. He didn't mention where he lived (or was living). Grammatically correct. All verbs backshifted. "Where he lived" refers only to the moment of the conversation (last week). version 1c - Last week, I saw my friend Joe for the first time in a few years. He didn't mention where he lives (or is living). Grammatically correct. Verbs that apply to the present and future are optionally not backshifted. "Where he lives" refers to last week, this week, and the foreseeable future. version 2a - Last summer, I saw my friend Joe for the first time in a few years. He didn't mention where he had lived (or had been living) since we last met. Grammatically correct. "Where he had lived" refers to a period of time up to the conversation last summer. version 2b - Last week, I saw my friend Joe for the first time in a few years. He didn't mention where he has lived (or has been living) since we last met. Grammatically correct. "Where he has lived" refers to a period of time up to the present. More information: https://www.thoughtco.com/backshift-sequence-of-tense-rule-in-grammar-1689017