The most recent thing that had been done to the file was editing in the New-Formats editor (and/or manual editing in the text Editor).
None of the levels from Lemmings Open Air was created in the Old-Formats editor, except for a level using my Autumn tileset called "Fallen leaves". But than one doesn't cause any trouble, and any later edits to it have been done in the New-Formats editor as well.
Note that this seems to be a problem specific to the NeoLemmix editor; the NeoLemmix player has no issues playing these levels. It's just that you can't edit them in the editor anymore. Which is even more dangerous, because this way it is possible to destroy a level (from the editor perspective) and not realise it because it is still playable in the player. Or, you might only realise it once it's too late, and all older backup copies have been overwritten.
But if we can find out where in the text editor file the issue arises, it should be possible to fix this issue myself whenever it comes up, without having to resort to replacing the level with an older version (i.e. before it broke).