There are vegetable oil based motor oils available. Having spent 10 years of my life making paint resins out of vegetable oil, no such concoction will ever go in any engine I own. Without vast quantities of additives, unsaturated oils polymerize. If you do a search, you should be able to find more of my ranting about it.
The original ester motor oil was castor oil. It is saturated and less likely to polymerize without modern additives.
Note, there are other polyols available to make esters besides neopentyl glycol. You can also esterify alcohols with polybasic acids to form esters. I think both are used in motor oils.