Don't trust engines; if you feel the move was good and the engine's refutation is not convincing, trust your opinion. Probably lichess felt that 15. e6! is strong for White though, as the pawn cannot be taken and after White plays f4, he can get a strong cramp. (In my opinion, 14... f6? is not such a good idea.)
Probably 26. Rd3 is not so bad for you instead of taking the pawn.
For him, the ending position is an easy win with 34...Qd7 35. Qc4 Qd3 and a trade of queens is forced.
Is there anyway black can win this endgame? I am spending a lot of time pondering this position wondering how it could have been, my opponent forgot to but the delay but I didn't want to take risks.