Which Clock Signal Does the USB Module Depend On?

The 48MHz are generated by a PLL. The PLL can be fed from either XT1 (if no XT2 supported) or XT2 (if XT2 supported). The USB module AFAILKK does not use nor need any other clock source (what should it be needed for?).
Anyway, the selected crystal must be there and running (enabled in the UCS module)

Well, it could be possible that MCLK is required for reading and writing to the RAM, but likely, the USB does the ram access based on its own 48MHz clock (with waitstates) and USB access to the ram will generate ram read waitstates when the MCU tries to access the ram at the same time.
The users guide also states that the USB module can only be active during LPM up to LPM1. So LPM2 and up, the USB module won’t work too.
Likely not because SMCLK or ACLK are required (else LPM2 would be allowed too), but rather because LPM2+ does not make sense if there is an energy-hungry USB module still running. (and therefore bus power available)
(LPM1 is allowed because it makes sense to switch the DCO off if you already have an HF crystal available and can run MCLK from there, which will turn LPM0 into LPM1)
It's also possible that LMP3/4 could switch off the crystal if not required for SMCLK/MCLK/ACLK, so USB can't work anymore.
However, the users guide doesn't tell the reasons, so it is just educated guessing.