Grammatically the but makes sense I think because of what was before that.
As she said she would be lying if she said she wants lonely (=the idea is her saying she wasn't lonely, But...) but could be wrong about that
Ah, I think I see where our thoughts diverged.
I believe what's going on for the context is the double negative: Senko saying "I'd be lying if I said I wasn't lonely" indirectly means "I do feel lonely, saying otherwise would be a lie", because of how the two negatives essentially cancel out each other.
But iirc due to how Japanese works, the direct translation at that particular point would be "but/however"? And grammatically "but" is fine too-it acts as a pivot point, albeit a slightly unusual one. So either way works, tbh. Ignore me and carry on, guess this was much ado over nothing lol