Q: Will Liriel Baenre ever meet Drizzt Do'Urden, R.A. Salvatore's signature character?
A: Gods above, I hope not!
Don't get me wrong -- I love Bob Salvatore's stories and Drizzt is a great character. But the only thing Drizzt and Liriel have in common is that they're both drow. They are SO different that any story about them would be dominated by the "enemies forced to make an alliance to meet a common goal" theme, which is one of the most frequently used notions in fantasy.
And who would write it? Neither author wants to write the other's characters, and a collaboration is not in the cards. Wizards of the Coast owns both Liriel and Drizzt, and I suppose they could assign such a story to a third writer, but I can't see why they'd want to. Let's face it, if RAS wants a drow companion for Drizzt, he's more than capable of creating his own.
Some time ago, I answered this question on a message board with the following hypothetical meeting:
Liriel: (Oo! Cute little drow toyboy! Thank you, Eilistraee, goddess of the butt-neckid moonlit dance.)
Drizzt: (Danger! Matron-in-the-making! Strengthen me, Mielikki, whose unicorn favors the chaste and virtuous.) ::draws his two scimitars::
Liriel: ::sniffs:: "Put away the cutlery, honey, and take a look at THESE twins..."
::At this inopportune moment, Catti-brie walks in; catfight ensues.::