Lexy's Labyrinth targets CC2-like rules by default ("Lexy" mode), but should be able to play CC1 levels as well. If a level really seems impossible, try using the compat mode for the game it was designed for: Lynx for a CC1 level (DAT/CCL file), or Steam for a CC2 level (C2M/C2G file).

Impossible

Every level from Chip's Challenge, Chip's Challenge 2, and every Chip's Challenge Level Pack should be beatable under Lexy rules.

More difficult than intended

CCLXP2 #54 (Killer Rooms *)

On the left side of the level is a block of chips surrounded by a swarm of bugs. The bugs are too closely packed together to proceed in a line as placed, so they exhibit some chaotic behavior before stabilizing. On both MS and Lynx (albeit differently), the stable pattern proceeds clockwise, with the bugs following along the outer wall. Under Lexy rules, the stable behavior has the bugs circling counter-clockwise around the chips/hearts, so naïvely collecting them is impossible — once only two hearts remain, there won't be enough room left in the swarm to swipe one without being hit.

The bugs can still be disrupted and the level beaten, but it requires slightly more thought (and timing).

CCLP4 #56 (Fireworks Factory)

Under Lynx rules, anything in an open trap is automatically ejected in its facing direction. This is a forced move, so if the actor can't leave the trap in that direction, it can't move at all. (This doesn't apply to the player, who can turn even while in a closed trap.)

This level has a row of traps near the top and a number of red buttons that spawn blocks to hold the traps open. After this is done, a fireball cloner activates, and it relies on the first fireball turning right, going north into the leftmost trap, and getting stuck facing a recessed wall. This would create a corner, so all other fireballs turn left instead of right, and ultimately detonate a number of mines.

Unfortunately, under CC2 rules, an open trap acts more or less like regular floor. The first fireball is allowed to simply turn right again and continue on through the row of traps, ultimately making a loop. The level is still possible, but it requires waiting for the upper area to clog with enough fireballs that several of them get redirected southwards and into the mines as intended.