Lizard Lip nickname

As Elliot said, alliteration is more important than anything here- for example in Spanish the bad guy could be "Lucas Labio de Lagarto" or "Lucas Labio de Lagartija". Whatever language you are translating to, definitely his nickname is just Luke lip of lizard, as you suggested.

It is common in cowboy storytellings to have nicknames for villains in order to build fear of, or hatred toward them. This serves the plot to make the conflict more dramatic and the victory sweeter or more satisfying. Alliteration is often more important that any kind of accuracy. Simple examples, Slippery Sam and Dead-eye Duke are a few that come to mind.

You're quite right. Bandit Luke has nothing in common with lizards.

Watching Hard Luck just now, it's obvious the only - and even that, irrelevant - reference to lizards is when our hero sets off to find the zoo an armadillo… that's it.

Including lots of the ladies, the Luke character looks to be the least lizard-like lad in the whole movie. His lips don't look dry nor straight or thin and he doesn't seem significantly unsmiling…

That some scriptwriter seems to have thought the alliteration more important than its possible meaning seems silly… but so is everything else about that movie, from the pointless title on…