How does one charge a 37-volt lithium battery?
The 36-37 VDC (nameplate) Li-Ion batteries are fairly common in electric scooters/ hoverboards e-bikes etc. etc. It looks like a typical Li-Ion 10S battery pack. There is a huge section of industry making them and equivalents. Example:



Since the battery is labeled as "smart battery" and has only 2 terminals, it means that all necessary balancing electronics is already built in, and the only thing you need is to get a proper AC-DC adapter/charger. Typical chargers provide 42V to charge these batteries, there are plenty of them on the market. From specs:


  INPUT SPEC:AC100-240V 50/60HZ 
  
  charging voltage: DC42V
  
  charging current: 2A
  
  Charging mode: CC-CV


The "CC-CV" means that this is a full charger. All you need is to make an adapter between the XT60 and the barrel 5.5mm x 2.5mm jack.