Lieberman isn't a RINO; he's an independent liberal. (The 'R' in RINO stands for 'Republican'). McCain won't pick Lieberman. No need -- has already has (most of) the center wrapped up. He needs to shore up the base, and he knows it.
How about Tancredo? Duncan Hunter
The chance of McCain picking Hunter or Tancredo (guys that got less than 1% of the vote in the primaries) is zero. I'd love to see it (I supported Hunter in the primaries), but it's a ganja pipe dream.
I think your analysis is right on target. If there's a motive for bringing up Liberman's name it to show how bi-partisan McCain is to all the squishy independents and to make conservatives happy when he doesn't pick him.
I will observe that IMO Cheney has been one of the best VPs we've had in a very long time and I don't see him having had much influence. Of course that could vary from president to president, but at least I can easily see Cheney being president and I can't remember the last time I felt that way. Given McCain's age I think it's important for the pick to not only be conservative but "instant president" material.
But I'll be doggone if I know who that is...