Any suggestions for lubricating O-Rings that are used for water pumps,
basically I want to extend useful life as much as possible. Someone
suggested lithium grease?

SD

Petroleum Jelly (Vaseline)

I don't think so---will eventually ruin the O ring

Depends entirely on what the o-ring is made from.

Most O-rings are Buna-n, some are Viton, others are Teflon.
Vaseline is compatable with all of them.

But, probably not a good choice for potable water, certainly not if in
contact (altho a minimal risk, isn't approved for food contact).

I'd ask OP _what_ o-rings, what kind/style of pump, etc., ...

Depending, may not need any lubrication and/or may be detrimental to
performance/longevity or may be water-lubricated or...

The small amounts of Vaseline that may enter the water will cause no
harm. Vaseline is non toxic.