Is sentence correct?

The second sentence is correct.

The first sentence could be improved but it does make grammatical sense, more or less. The second sentence could be used in a context where the speaker is recounting past events. Picture two friends speaking to each other. One says, "Remember how lonely I was when I moved to this city three years ago? I didn't have many friends. I had not yet met Alice or Billy or Chuck. In fact, you are the only person I knew who lived here in the city."

Grammatically, it's not perfect. In this hypothetical context it would make more sense to put all of the verbs in the past tense: "You were the only person I knew who lived here in the city." But the sentence is not quite grammatically wrong either. If the speaker is deliberately trying to emphasize that his statement is being made in the present and that he is addressing his friend as someone in the present ("You, the person standing in front of me right now: you are the only person I knew who lived here in the city."), then the sentence could be considered grammatically correct.

Many thanks for the lucid explanation.

All the best.