I'm unaware of a lithium A76, S76, P76, KR76, LR44, SR44, 375, ... battery. As you can tell, there are actually many designators for essentially the same battery. Yes, there is a difference in chemistry among them (to an extent; silver oxide, typical alkaline, even zinc-air which hasn't been mentioned yet). All will have an optimum discharge at some point during their life and less-than-optimum at other times. That's usually at the beginning and end of life. This was the reason for mercury batteries in the first place...flat discharge curve for most of lifespan.
The upshot. You can use any of these batteries that have the same form factor and nominal voltage of 1.5v to get adequate results. I used silver oxides in my XA for a long time and got perfectly exposed kodachromes and ektachromes every time. I recommend AgO batteries if you can get them for a decent price. $12 for 1 is highway robbery.
Like most people here, I also have many other XA, XA2, and I think XA3. Yes, with the A-11 flash in most cases. Clearly, too many XA's for one person. I'm downsizing....slowly.
Enjoy your new camera. It will become a friend.