This is one of a class of Martian craters where the history goes like this:-

1) large impact early in Mars' history (note crater size is in the 80-100km+ diameter range - Those cracks are several to tens of km across - not little lave tubes)
2) Infill of crater by layered material, including volatiles (ice of one sort or another)
3) Regional tectonics leading to cracking of the surrounding plains and the crater fill
4) Substantial collapse and erosion of the crater fill, eating back the edges of the cracks

In some cases, large areas of *Chaos* terrain are generated by this process. The features we see aren't lava tubes and don't predate the crater.

But these types of features are part of the widespread behaviour of ground collapse and pit development on Mars that may create subsurface voids (caves).

Near-surface open caves are likely rare because of the rain of impactors over Mars' history, bashing the ground like the hammers of angry giants. I have been impressed by the Spirit (and to a lesser degree, Opportunity) images showing geological formations that are all smashed up, cracked, and brecciated to varying degrees by this slow but steady hammering process.

A cave needs to be strong and young to survive on Mars, and the best areas are where relatively recent vulcanism is proven by relatively uncratered flow surfaces and collapse/tube features like that linked by Raoul.