A funny counterexample where there IS a problem, i.e. where Lichess would not follow FIDE rules : This position (black to move)...
lichess.org/analysis/fromPosition/k7/Q6r/2b5/1pBp1p1p/1P1P1P1P/KP6/1P6/8_b_-_-
... should be declared a draw if either side times out - it is unwinnable. But Lichess would probably not be able to see it. There's no legal series of moves leading to checkmate, despite Queen, Rook and two Bishops on the board.
(Example form the "unwinnability analyzer" homepage. Such positions are extremely rare in practical games.)
lichess.org/analysis/fromPosition/k7/Q6r/2b5/1pBp1p1p/1P1P1P1P/KP6/1P6/8_b_-_-
... should be declared a draw if either side times out - it is unwinnable. But Lichess would probably not be able to see it. There's no legal series of moves leading to checkmate, despite Queen, Rook and two Bishops on the board.
(Example form the "unwinnability analyzer" homepage. Such positions are extremely rare in practical games.)