I am trying to research the proper circuit that has been proven to work using 4v Li-Ion 2s2p for each pack on the Neato XV but I am having trouble finding it.
There are many such circuits made by hobbyists, such as my posts on LiFePo4 adapters in this thread, as well as German hobbyists. Circuits without logic simulation of NiMh thermistor signals (which control NiMh charging compared to voltage only with lithium) work using a balancing circuit for multiple cells, which heat up to operate the normal thermistors. A large balancing current is needed, not always supported. This became less practical when balancing products became more efficient and cooler, but see the other thread on LiFePo4 in the Botvac
where one was used.
The commercial LithiumPowerInc / AnewPow XV batteries have a proprietary adapter with fairly sophisticated logic, maybe a microcontroller (8 pin ones are very cheap now). It takes only a simple voltage comparator of the type used in power supplies to translate charging voltage into a thermistor signal at the maximum lithium point, sufficient to control the charger but refinements can be added, along with protection.
A battery supplied with only protection circuits would have to be used with the unpublished USB command SetConfig BatteryType 3 to convert the Neato charger to Vorwerk lithium, voltage regulated mode. The NiMh charger stops when temperature rises faster than 1C/min, and at higher voltage dangerous for lithium (protection circuits cutting out produce error msgs.) Only good on the newer, Rev64 Cruz system boards used several years now -- dropping the original extra side jack for charging. These have been made by hobbyists and are best done with the newest, safer chemistry LiNMC cells. Higher energy density than other safe forms LiNMN etc. some Germans used, or the longer lasting LiFePo4 density too low to fit enough cells.
Due to the critical role of quality control for safety with lithium ion cells (potential for runaway positive feedback self discharge with contaminants), brandless unknown Asian batteries are for flashlights, not electronics so much.
LithiumPower Inc has a reputation as suppliers of adapters in medical equipment and years as suppliers for Roomba products. (Even the major suppliers have problems now given Samsung's debacle, due to an over complex supply chain insufficiently managed, as well as rushed designs not fully tested and developed. IBM is pioneering more sophisticated supply network support, capable of tracing all parts back to origins, presently not available -- except in the space program.)
I don't think Samsung's problem affects the large cells needed for vacuums, as it involved trying to squeeze the size of cells for compactness in a data tablet.