This could probably be a sync issue.

Player should be able to get it to start syncing again by deleting the cloud save data from:

iCloud: Settings app -> (your apple ID) -> iCloud -> Manage Storage -> Lemmings: The Puzzle Adventure -> Delete Data

The warning says it's going to delete all of the data for Lemmings, but that's a lie. The game uses both iCloud and local storage; the copy of the save game that's in local storage won't get deleted.

This way, when player re-opens the app after deleting the data from iCloud, it'll be that save file that gets re-uploaded to iCloud and your device should then hopefully sync correctly.

The last resort is to reinstall the game but player may lose the data saved in this process so make sure to take the screenshots like screenshot of the last level gameplay where world and level number is displayed at the bottom, screenshot of boosters and tribes completed, coins earned etc. so that in worse case scenario if any items are missed out, we can compensate them for you.