In addition to the "single-serving" mechanical features that Uwe's answer describes, the guidance programming for the LM's onboard computer doesn't support any ascent flight on the descent stage.
In particular this means you'd have to go to the manual throttle mode, P67, to lift off, then switch back to P66 to land again. The switch to P66 would have to be done while the spacecraft was descending, not ascending (I don't have a citation, but I've been told that the LM would attempt to turn upside down if it was moving upward in P66). Here's a nice overview of the Apollo LM guidance programs.
Getting off the surface, to an altitude and velocity safe enough to switch guidance programs, then landing again, with whatever propellant was remaining after the initial landing would be extremely risky, and it was never considered or trained for -- but I believe it would have been physically possible.
I disagree with Uwe that the contact probes and landing gear "crush cores" would be needed to land.
The probes were actually intended to keep the engine from being shut off too late, not too early; there was concern that running the engine all the way to touchdown would risk kicking surface material up into the spacecraft and causing damage, so the mission plan called for shutting off the engine a few feet above the surface. On A11 in particular, Armstrong didn't consciously react to Aldrin's "contact light" call, and ran the engine all the way to touchdown, or very close to it, and no particular problems occurred as a result:
Aldrin: "I called contact light."
Armstrong: "I'm sure you did, but I didn't hear it, nor did I see it. I heard you say something about contact, and I was spring loaded to the stop engine position, but I really don't know whether we had actually touched prior to contact or whether the engine off signal was before contact. In any case, the engine shutdown was not very high above the surface."
Lifting off and landing again would have been mechanically fine, assuming that the initial touchdown hadn't done any damage to the engine bell. Without the probes, the crew would rely on the radar altimeter and the physical impact of the footpads on the surface; it would be another very soft landing.
As a result of Apollo 11's soft touchdown, the crush cores in the landing gear were barely affected on the landing. This is the reason the LM crew ladder ended so high above the footpad -- it was designed to stay just above the surface if the entire shock absorber core was collapsed.
In a situation such as your "breaking crust" hypothetical, or the LM starting to tip over, or any other situation that would call for an urgent liftoff, the done thing would be to stage the LM, lift off with the ascent stage, and abort the mission.