Standing behind my usual claim of ignorance, I'd guess that NiCd would be fine in the APU-battery role, and it's lithium just to keep the LRU count down. The real requirements for the two batteries must be hugely different.
The official explanation is that the Li battery can deliver enough power for several starts of the APU and then be quickly recharged again once the APU or other power source is running. NiCd's higher internal resistance makes very rapid recharging more problematic.
Using the same battery for both purposes is a little harder to justify, but in terms of design, testing and acceptance seems plausible.