My A/C has issues on my
L4060. But every time I check it's because the condenser is plugged. Dust & dirt packs in there pretty good at times. Its not always that obvious either.
I wouldnt get a lithium battery for a tractor. I have one that would likely fit that I got for mobile HAM radio stuff. Charging voltages are different enough you shouldn't swap the 2 types unless you get one designed for drop in automotive type use with a proper charge controller.