Mostly thanks to DireKrow, it is now confirmed that all official levels are solvable in the latest build of Loap.
As for Lemmings Plus 3D, all Fun and Tricky levels are confirmed solvable except for Tricky 22 "Redirect Loop", which is unsolvable due to a physics bug. The Taxing and Mayhem levels remain mostly untested, although Mayhem 79 "Power Distribution" is also unsolvable, in this case due to an intentional physics difference (once I do a proper conversion of the pack, I will adjust this level as necessary to restore solvability).
The only levels I can think of off the top of my head that are explicitly confirmed solvable in LP3D Taxing and Mayhem are Taxing 45 "Deathspring Tunnel", Taxing 56 "Ultimate Lemja Warrior" and Mayhem 70 "Detour Shot". This does not mean the others aren't (except, as noted above, Mayhem 79 "Power Distribution"); just that they're not confirmed either way - it is very likely the vast majority of them are solvable. (EDIT: On further thought, Taxing 53 "Complimentary Lemmings", Mayhem 64 "Candy Corner" and Mayhem 71 "Kingdom Of Chaos" are also confirmed solvable.)