If you're referring to white lithium grease, there are lots of better greases than that, just not as commonly available.
I used to use white lithium fairly regularly for various mechanisms, but found that it always dried out over time, and seemed to attract dirt when used in open locations.
I've seen lots of comments recommending and praising ordinary wheel bearing grease, which is probably better if it's not white lithium. Then again, some folks will claim that anything that costs less is the best product.
For different types of machine applications, it would probably be wisest to visit a manufacurer's dealer/rep to get a guide for their different greases and lubricants (Pennzoil, Valvoline, Wolfs Head, etc).
Distributors such as Fastenal, Applied Industrial Technologies, and other industrial parts vendors probably have guides for lubricants.
I can't recall white lithium grease ever being recommended for lubrication in any service manuals.