Origins of level names
I won't include some that are just obvious puns on well-known expressions.
Touchy 1 "Deep Trouble" - This is a reference to the Crash Bandicoot 3 level of the same name, although the levels have nothing else in common.
Touchy 6 "Born To Lem" / Touchy 7 "World is a LEMMING" - This is a reference to the "Born to die / World is a FUCK / etc" meme.
Edgy 9 "The "What The Lemming" Machine" - Although probably not noticable, I was thinking of The "Oh My God" Particle when I named this level.
Edgy 10 "POOR BEE CREATURES!" - A reference to Taxing 28 of Original Lemmings "POOR WEE CREATURES!". And of course, a bee pun.
Edgy 15 "The Hard-For-Flopsy Level" - This refers to an in-joke in the #neolemmix chat where levels featuring tight time limits and high release rates, especially with lemmings facing immediate danger, were labelled "Hard-For-Flopsy levels".
Unruly 14 "Lemmonition" - Only listing this one because someone thought it was a different wordplay; it's a play on "Premonition".
Unruly 15 "Abstract Art Gallery" - A reference to Taxing 8 of Original Lemmings "The Art Gallery", combined with this level being in the Abstract style.
Outrageous 13 "Lost In Blue" - A reference to the Nintendo DS game of the same name.
Outrageous 15 "To Infinity, Beyond And Back!" - A reference to the phrase "To infinity and beyond", combined with the fact that the exit (initially locked) is very close to the starting point.