To be clear: even the regular "multi-purpose" Superlube grease is not lithium based. Just a different synthetic, with PTFE in it. Though, I'd guess a regular lithium grease would be okay too, but might not last as long, because it will get gummy sooner.

I'm no expert on use of grease in pins, but I suspect that the warning about silicone is because silicone-based grease, and other silicone-based products, can be harmful to paint and possibly other non-metal components on the machine. Maybe someone who knows more specifically will explain.