I don't know that I'd have used lithium battery, rather just a standard 350cca lead-acid battery. Cheaper, works, and no chance of the li-ion battery damaging the regulator and/or stator. Extreme temps also can severely degrade the li-ion battery's performance.
If you're dead set on the lithium battery, you may have to figure out how to find/make a regulator work that will charge the battery at the correct voltage that they want. The factory regulator only charges 13.3-13.5v from what I remember of them. Some Li-ion battery companies want up close to 15v to charge them and they are pretty sensitive to that from what I'm seeing in the powersports world. I've done two regulators today alone on Polaris stuff, both had lithium batteries. I inquired about it directly from Polaris and they don't approve of li-ion battery use on anything other than what came with them from the factory which is the Ranger EV Li-ion and the Ranger Kinetic at this time. Those are the only two.
On 1760's I'd reccomend replacing the fuel pump. New pumps have a nipple on the bottom that you put a hose on, and run the hose down the side of the frame. The original pumps had a weep hole only and if/when the pump fails and leaks fuel out of the weep hole, it leaks directly on top of the muffler and you know what that leads to. A completely burnt mower, and shed, or whatever else is around it. Kubota and Kawasaki had a bulletin out about this a number of years ago.
if/when you pull the carb for cleaning, you also will need to remove the linkage plate from the block in order to get the linkage to come off of the carb. That or bend the linkages. Ain't no other way. When you put the linkage plate back on, the bolt holes are slotted which gives you the ability to adjust the fast idle RPM; which should be around 3450 RPM +/- 50. Additionally sometimes the little "horn" (elbow) that connects the carb to the air cleaner housing, there are two bolts that hold it to the flywheel housing. The nuts are captive in the flywheel housing and the nuts will sometimes spin inside the housing. If that happens you may have to replace the housing and the elbow after you cut the bolts off, and that housing is no longer available. So be careful with it. If you need parts, look at John Deere...the LX188 used the same engine. Great engine if taken care of. 3 major issues with them (or potential major issues), one the carb elbow bolts, two, plastic camshaft gear that sometimes knocks the teef off (and just stops running but you have to totally remove the engine to access the cam), and water pumps that will sometimes fail and fill the crankcase with coolant, then overheat. Overheating, lack of oil, and neglected air filters are the nemesis of these engines. Keep up with the maintenance and repairs, and they'll last nearly forever. I called them the 300 six of lawn mower engines. DId not make a lot of power but they'd run forever if you keep oil and coolant and air filter maintained. Oh and do a valve adjustment once in a while too.