I do not think the lithium battery is changing, rather the robot modeling of the battery properties, just a guess. Lithium batteries do not require conditioning the same as NiMh as far as I know, could be wrong. The robot is not equipped to measure the battery fully for lack of a load to discharge it on the dock like a test instrument, so it makes assumptions based on specifications for the original battery. Batteries have a curve along which voltage falls slightly as discharged, used to detect an over-discharged condition. The robot also measures the charge usage when run and when charging by integrating current x time continuously, IxT (the Botvac
has a special IC for this). Batteries also signal when fully charged by special temperature or voltage conditions, separate from the charge added.
The discharge curve for lithium batteries is more flat but lower than the curve for the original NiMh battery, so exactly what happens to the software, unpublished, is unknown except to companies who have reverse engineered it. The run time charge usage is programmed about 2ah, preserving an original large margin against damaging deep discharge, and a reserve for returning to base. As the battery ages and loses capacity, the software may detect premature discharges from monitoring the voltage discharge curve and comparing it to the measured charge usage over time, and adjusting programmed charge usage accordingly, to maintain reserves to return to base. So the "New Battery" option is just to signal an unknown battery is installed which is assumed to be the specified original battery. The system is more complicated than a simple flashlight with its need for a reserve to return to base and hence monitoring the battery capacity, charge and usage.
The NiMh batteries also had a situation where initial capacity could expand over several initial runs from a shelf-life problem of self-discharge in that chemistry, absent in lithium batteries (fixed in small AA size NiMh cells but not the larger higher drain types). The cells loosen up with initial use, mentioned in the manual (in some cases damage is irreversible, duds). So exactly what happens between the lithium batteries and the NiMh modeling software is not known. The more flat discharge curve has been observed to increase the run time over the NiMh probably from fooling the software certain ways. Initial short run times with the lithium substitutes has not been much reported and there could have been some defective condition in the lithium adapter board microcontroller and its software. Lab facilities would be needed to tell, digital instruments etc.
 Experiments with DIY batteries showed the Neato's get better measurements of the battery when initially charged from a mostly discharged condition, so measurements of the charge added are more indicative of the capacity. The charger tends to remain in the orange blinking state until 1ah charge is added to the battery.