Good onya Dave ^ lol
Seriously tho, I think OP is getting at that some folk put linseed oil or some other oil on the wood (like for baseball bats/cricket bats) to stop them splitting (drying out).
Ball hitting bats are hitting balls with enormous force, often (if the batter is any good)
and most bats are raw (not laquered/varnished) so they will dry out and you have to keep them oiled.
Handgun grips should be laquered thats why they are so purdy to look at, so they dont need oil IMO. Oil on handgrips is not a good idea for obvious reasons (slipery)
What you MIGHT want to do tho, is put a little quality 'furniture (wood) polish' on the grips, so the polish fills any little nooks & crannies.... rather than your hand sweating (or if your hand gets dirty) & this sweat and crud finds the nooks & crannies, then you can never get the crud out & your grips will end up looking dirty & you can't clean it out
If you do polish them, test it on the inside of the grip first, to make sure the polish doesn't 'react' with the laquer (& make it a horrible color or something) If it is ok, rub the polish well into your handles, then buff it off well too (so it isnt slipery)
I have done this with all of the rosewood & walnut grips on my Pietta's and Vaquaros & they look like they are still new, even tho I have handled them with hands dirty from Black Powder.
So, IMO, no oil, good quality furniture polish... way to go, I reckon