Why did my opponent get a win when he had only King + Bishop?

My latest game I ran out of time where I had K + B + 4 pawns, and my opponent had only King and his light-squared Bishop... is it not impossible to deliver checkmate with only the King and the Bishop? Should this not have ended in a draw, even though I was the one who ran out of time?

Say White has the K and a light squared bishop. Put the Black King on a8, and promote a Black pawn to a dark squared bishop. Put the White K on a6 and the Bishop on c6, and the promoted Black bishop on b8. Checkmate. If you can create a checkmate by any series of moves, not matter how illogical, you lose. a player once lost R+K vs K+N because he ran out of time. I'll leave it to you to create the mate with the N.

You are right, it is not impossible.
There exist legal positions where the K+B mates the K+B+4pawns.
For example lichess.org/analysis/8/8/1k6/1P6/KP1Pb3/B1P5/8/8_b_-_-#2

58...Kh4 59. Bc6 Kh3 60. Kg1 h5 61. Be8 h4 62. Bc6 Bg3 63. Bd7#

The R+K vs N+K was in an international FIDE OTB tournament, BTW.

lichess.org/editor/8/3B4/6p1/3p4/7p/5K1k/7b/8_b_-_-
A series of legal moves exists that leads to checkmate, hence you lost on time.
If you do not like this, then play with increment.

Where do you draw the line having a single lightpiece?

Piece vs. piece is admittedly a likely draw (but remember: if the million monkeys play infinitely...). If one party has more material „smothered-type“ mates are more likely. Even in the Megabase you‘ll find single piece wins.

This „helpmate-minus-1“ complicated matters in the past.

So this (FIDE, playchess, lichess) is the lessest evil.

This is annoying especially in games on low time. Because the opponent can play on time even if the position is a draw. For example bishop pawn and king against bishop and a king (both bishops are lightsquared)

This topic is so common it should have its own category on the forum page.

General Chess Discussion
The place to discuss general chess topics

Game analysis
Show us your game and let the community analyse it

Lichess Feedback
Bug reports, feature requests, suggestions

Off-Topic Discussion
Everything that isn't related to chess

Draw by insufficient material.
Complain to us and we will explain what this rule actually is to you.

Let me tell you a secret: if you cannot stand playing chess without increments then you can play with increments. No prob.

PS: case #8 has nothing to do with the „new“ rule. This has always been that way, you can try to flag your opponent in non-winnable positions. Online and offline. Remedy: INCREMENT!