Yes, you can make the current flow from the battery cut out at the optimal level for the lithium battery.
BTW, it can also be use to protect lead-acid batteries from going too low, and thereby protect them.
I have one in my car in order to ensure that the fridge doesn't take the voltage too low, and thereby ensure that the car can always still start.
But there is still the issue of whether the charging circuit in the UPS is optimal for the lithium battery. But this is a common problem, lead-acid, AGM, lead-crystal and lithium batteries all have different charging profiles.
The gadget does however ensure that the lithium battery voltage doesn't go too low. Read the link that I gave.
There are different brands of these gadgets, I also have some others.
Another example :
Smarter Shopping, Better Living! Aliexpress.com
www.aliexpress.com
Some of the car fridges and other devices, as well as UPS's, have built-in cut-offs, but they invariably cut off at too low voltages, thereby causing damage to the batteries. One of these gadgets will protect your batteries.