They were both played by Majel Barrett-Roddenberry, but I can't remember if she ever interacted with a Federation computer. Which would be a nice in-joke if it happened.
Twice in fact.
LWAXANA: Hello, computer? Is Commander Riker still on the Bridge?
COMPUTER: Negative. Riker is currently in holodeck three.
LWAXANA: Holodeck? Where is that?
COMPUTER: Follow the comm. panel lights. They will lead you there.
LWAXANA: I'll bet you've never been to a colony of free spirits.
ALEXANDER: What do they do there?
LWAXANA: Whatever they want. Artists, philosophers, free thinkers and people who don't quite fit other people's rules. Personally, I come for the mud baths. You, oh, you're going to adore the mud baths. Computer? I'm assuming you have the Parallax Colony of Shiralea VI?
COMPUTER: That programme is available.
LWAXANA: Oh, good. Then run it for us, dear.