Incorrect Game Result : Draw When My Opponent's Time Ran Out

Endgame : His K+R versus my K+B. I offered a draw to my opponent. He turned it down. Probably hoped I'd line up my B with my K so He could get it with his R. We played on; I made no such mistake. His clock expired. Game over, but the box score recorded 1/2 point for each. I'm new to Lichess, but if this is your idea of fairness, I'm gone. What happened? Can this be corrected?

you cant evantually checkmate with a Bishop, so this should be a draw

In a tournament, wouldn't I win if his clock ran out? Not draw? Timed chess is timed chess, no? I offered a draw to save us both time, and I think he was rather arrogant to turn it down... Implied I was a dolt. I really need to know if this was in a tournament, would it be a draw?

Yes, this is a draw. Read up on the rules: http://www.fide.com/component/handbook/?id=124&view=article

Section 1.3: If the position is such that neither player can possibly checkmate, the game is drawn.

Player 1: Does not having enough time = cannot checkmate
Player 2: Does not have enough material = cannot checkmate

Therefore the position is drawn.

I really did not know about the draw result in this particular situation. Aside from his arrogance in assuming I wouldd make a fatal mistake, it makes sense the way you depicted the rules. I've played chess all my life, but I guess I never encountered this before! Thanks.

Yes Pedro, but with a rook he would be able to interpose. This is a clear draw according to rules and the universe.

In the USA (where they use USCF rules) it would not be a draw. This is because a help-mate is possible, and therefore it can only be drawn by stalemate or repetition claims or eventually the fifty move rule.

Thank you. What would have happened in my online game if MY clock had run out..? I suspect I would have lost (K+R can mate if a mistake is made playing K+B)...?

You would lose because your opponent has mating material. But if he had a king and three knights, or a king and two knights or a king and one knight + a bishop, it would be a draw! :-)