I'm familiar with Fluid Film, in fact they are a customer of mine and they gave me can a while back to try. I have used it but not extensively, the major benefit is that it doesn't dry out. Yes, it's made from sheep, their facility in S. San Francisco smells like wet animals, that's not to say the product is smelly but it does have a unique odor.
White lithium is one of the poorest lubricants overall in my experience. It works fine when first applied, but it dries over time into a very hard stinky cake that has to be chiseled off when you go to figure out why the window gear works so hard. My favorite in the past for a lubricant that I want to hold its qualities in many applications is wheel bearing grease. It seems to adhere tenaciously to the parts, and maintains its ability to coat and make parts slide on each other for decades.
That said, your question inspired me to Google, and that led me to learn of a product I had never heard of before. It's called "Fluid Film". It seems to have great cred in the marine industry. and sure seems like it would do an excellent job of maintaining its lubricity characteristics over time. Interestingly, it is largely an organic - lanolin from wool - rather than being a petroleum-based formula with VOCs that dry out over time. Looks like it's widely available - Advance Auto, Carquest, John Deere, etc. Did any of you 300 folks ever use Fluid Film, and is it as great as the testimonials would indicate?