As-is, it won't, but that doesn't mean there won't be some way to convert it. Have you played the PS2 version? From what I can tell, it appears to be more or less a direct port of the PSP version except with EyeToy mode added - if so, it's very likely that the internal format is the same, and that there'll be some way to convert them.
I don't have a PSP, and haven't had too much luck trying to get Lemmings running on either of the available emulators (another reason to try using the emulator to convert the format even though you could just run the game directly), but I do have a modded PS2 so getting access to my save data (in raw format, rather than some cheat device's encoded format) or getting a copy of Lemmings for it shouldn't be a problem. My PS2 is only software modded which usually can't run CD games (and Lemmings is one of the few PS2 games that uses a CD disc), but there's a way to convert them to DVD and I remember getting Lemmings working successfully in the past that way.
If I were to look into this, would you be able to help if needed? (Help would most likely be limited to sending me levels you've made (maybe in some cases specifically designed for the purpose), and testing ones that I send you - no technical knowledge needed.) Not promising anything, but if there's interest in it...