I think the lock says not to use rechargeable batteries because their operating voltage is too low and these locks need at least 1.35v to 1.5v operating voltage. Note that these are Lithium and not Lithium Ion batteries, different voltages.
See this voltage curve for a comparison between the various batteries. You’ll notice the issue with the NiMH batteries and even alkaline batteries. The voltage drops rather quickly and which causes issues with lock operation.