I have never known a lithium battery to leak - doesn't mean it won't, but i have not seen.
I have never known alkaline or carbon batteries to NOT leak. And, no one should ever buy a carbon battery.
I have done the best as can be done with my LunaPro SBC by fitting it with a lithium 9v battery. Long lasting and never leaking. I found Kodak batteries - don't know if others make. I had a Kodak lithium battery in a digital voltmeter since 1987 and didn't replace the battery until i bought the lightmeter in about 2011. It was perfect - i bought two to outfit both devices plus a spare each in one order!
By the way, lithium metal is very light, and that results in a super light battery package compared to any other battery type (possibly zinc-air is lighter), plus, the power density of lithium chemistry is superior to any other. The military has been using lithium in batteries for many, many years.
As far as i know, it is not possible to make lithium chemistry work as low as 1.5v, so i think they are available only in 3v and up packages. So if you buy an "AA" lithium battery, make sure the "AA" does not refer to the size only. My view of calling a battery AA is that it is a 1.5v battery in the AA size.
Old batteries (with the possible exception of lithium) should be thrown out (in appropriate waste stream) even unused. I appreciate that Duracell have a great big label with date expires on their batteries. Follow that advice religiously if you value your equipment
It is probably a good idea to replace every battery in every photo device yearly (except lithium) just as we are advised to do so with our fire alarms. A safety best practice that will pay for itself in unknown catastrophes - imagine losing a camera, or worse, an image on film because of battery failure! I shutter (sic) at the thought of losing a "mona lisa" negative.