Not every power management system is able to charge a lithium battery.
Lithium batteries rest and charge at roughly 1 volt higher than an AGM battery. While this doesn't sound like a lot, what this means is that if you try charging a lithium battery with a non-lithium compatible battery management system, it will only put a charge into a lithium battery until it is around 80-90% full. This is due to the charge voltage and current not getting high enough and long enough, as the battery charging profile for these kinds of battery management systems is for wet-cell only.
This also means that the coulomb count, which works off voltage and current to give you an accurate time remaining, will be out as well, due to the voltage of the lithium not matching the wet-cell profile.
For example: A lithium battery holds its voltage at 13.1V when in use, even at 50%, compared to an AGM battery at 50% which is around 12.2 volts. The power management system will see a higher voltage than what it was expecting, and will not charge the battery as it thinks the battery is full, as the rest mode of a AGM battery is 12.7- 12.9V. The coulomb count may also be out at this point, the battery may rise to float at 13.6V, which at is the minimal current to maintain an AGM near full.