You're being overly pedantic either for comic effect or because you're an OCD idiot.
Lithium (and presumably something else, a battery needs two chemicals doesn't it?) makes coin cells you can't recharge. Then came several variaties of rechargeable Lithiums. Your favourite is the Po, but there were many before it. There are still at least three types on sale. I hear of LiFePo for example. Reality check - when someone says "a Lithium battery" they are quite likely talking about a rechargeable one where Lithium is one of the components, it could be LiPo or any of the others. As in "my electric car runs on Lithium batteries".
So why do you love them so much? Lead Acid doesn't catch fire, it's full of water.
Well this one did. Only about 3 years old, bought new.
Sounds like a totally s*it battery design to me. And as I've already said, if I were to connect a Lithium battery to a bench supply set to precisely 4.2V and leave it forever, the trickle current to a 3Ah battery would be about 10mA. I doubt that would cause damage.
Try this: Stick your phone in your back jeans pocket. Fall over onto something hard like some concrete steps outdoors and snap the phone in half. Try to get the burning phone out of your pocket before your buttock is singed. Yes it's happened, I've seen the youtube video.