Ummm, news to me. I've used lithium-based greases for all kinds of bike lubrication needs for over 40 years, with zero negative effects. Elemental lithium in oxygen is explosively reactive, but in the form of lithium soap, it is about as inert as any compound that exists. Keep in mind that the lithium soap is not what provides necessary lubrication, but it is the oil suspended in the soap.

But I'm not a true lubrication expert, only a chemist and a chemical engineer. For the deep answers, you need a tribologist - a lubrication expert.

My only other practical advice is that you can buy lithium-based greases in one-pound tubs at XMart for about $5. Or you can buy the exact same grease in one-ounce tubes at your LBS for $8. Second, I have used organic-based greases, in which the oil (petroleum-based) is replaced with some kind of plant-based derivative. They were useless. The oil and soap separated prematurely, then the oil leaked out (onto your carpet), eliminating the lubrication.

A general observation: water-based degreasers and non-petroleum based lubricants are useless. Look at the basic chemistry: they just don't work.