I've built several lithium battery packs myself and even documented the journey on one of the packs.
1st the cart and motor does not care where the power comes from as long as its in the acceptable range voltage/amperage for the controller and motor.
2nd I would steer clear of "drop in" conversions that use 4-6 batteries. To many compromises are made for them to fit in the original holes.
Check out RoyPow S51105. It is a purpose designed 105ah lithium battery which should give you a conservative 50 miles depending on tires and driving style. It should cost around $1,850 including the installation kit and charger. I believe that Advantage Golf Carts in Orlando/Ocala is a dealer and doing the installations for around $400.
Here's my build thread. Something like 26k views now. Lol
DIY 101 - 14 cell Nissan Leaf lithium pack