Drawing a match with a mate in 1

And even so, you can checkmate in a K+P vs K+.... position (aka promotion).

How unsportsmanlike. You should've clicked the "+15 seconds" button a hundred times.

The problem with clicking "+15 seconds" (or my earlier idea of having some way to disable autoflag) is that your internet connection might go down.

Yes, this sort of thing is unfortunate, but as Clarkey said, without having an adjudication system there's no way to award a game like this. Even with FIDE, you have to demonstrate to an adjudicator that there is a mating line possible with the position on the board in order to get awarded a win on time with what otherwise appears to be "insufficient material." With no way to demonstrate that to a judge, it's very difficult to have such wins awarded.

I believe FICS has an adjudication system for such things, where you can request a human adjudicator to view the game and explain your case for a game result change. However, I don't like it. If you play 10 more games afterward, and then your rating suddenly changes from that game 10 games before, it can't apply to all those other games you played, and so others may be losing more rating than they theoretically should have. Not to mention how many hundreds of people would we need to have adjudicating games, since I'm sure there would be a ridiculous amount of adjudication requests if the option were made available, simply because people always suspect cheaters, and it would confuse players as to whether to report the cheater or request game adjudication (on FICS both are handled through adjudication). What a moderation nightmare!

I don't know how difficult it would be to implement, or how much lag it would create, but could there be a way to potentially implement an adjudication flag that would simply have the position searched in an endgame database and change the time result from drawn to won if it finds a known forcing sequence to a win?

Databases won't solve this problem. Consider this (absurd) position:
N
P
P
P
P
P
P
KBk b
Black mates next move with Be1-c3# regardless of White's move. But there are too many pieces for this to appear in a database. You'd need to do a mate search to find Be1-c3#.

OK, what about an engine analysis? It could be an option only available for draws awarded on time out due to "insufficient material" that runs the engine analysis and if it finds mate from the final position, it changes? Again, I don't know how difficult it would be to code, nor the sort of resources that it would entail. Would it be a potential option though?

As far as I can imagine, it'd be evaluating the final state of the board to see if it's a mate in one or not, then adjudicating based on whose turn it is, but I'd hardly imagine it to be anywhere near as 'simple' as that. Evaluating every end position for every game on lichess is really going to add up...

No it won't. The insufficient material ending is an edge case. ALL end positions won't be evaluated.

That's what I was thinking...if it could be coded to only do a final position check for a forced mate (doesn't even need to be mate in 1 as there could be maybe a forced mate in 2 or 3 or 20 even and in theory that should also be a win for the player with clock remaining) for those extremely rare cases in which the game is drawn by insufficient material, I don't think it would require too many resources...also, like I was saying, maybe it could be an optional flag that only appears to the player in the event of that situation that they can click for adjudication (i.e. the engine check). Thoughts? I mean it seems to happen so rarely, I can't imagine it's a priority, but it would be something to slightly improve Lichess, no?

The difference with a FIDE match is that you can demonstrate to the arbiter that you in fact know how to win such a position, but even if the engine sees "mate in N" it doesn't mean the user knows how to carry out that mate sequence, its a complicated situation imo