Col. Playdoh said:
No need to speculate, for I can set forth the process in a few words. Larry Niven's writing had nothing to do with the creation of the Illithid race for the AD&D game.
I happened to be thinking of devising a new terrible race if creatures inimical to humans, and my eye fell upon a paperback book authored by Brian Lumley, The Burrowers Beneath. The cover illustration was of a bipedal monster with a head resembling a squid or an octopus. Voila!
That was a perfect model for an underground-dwelling race of fiendish predators on humankins, and thus the mind flayer was born.
I made up all the details of the race, of course, they being a form of AD&D monster.
BTW, the drow were inspired by no more than a dictionaly listing for the name as "dark elves," and i made up the kuo-toa out of whole cloth so as to have another underground race on distinctly non-human sort.