Liara is an introvert, but not cripplingly so. She opens up to Shepard regardless of whether or not she has been romanced. And she befriends everyone else on the Normandy as well, even less agreeable characters like Javik. She seems to get along with most, if not all of those crewmembers.
As for the fact that she doesn't find anyone to date if unromanced, I think that can be attributed to two possibilities: one, she's in love with Shepard regardless of what you do. Or two (and the more probable answer IMO), she doesn't have much time for or interest in pursuing side relationships during the events of the trilogy. Especially since she's canonically a virgin at the start of the trilogy, which seems to make her more apprehensive about topics like love and sex than she might otherwise be.
She's also not the only squadmate who ends up alone. In fact, the majority of them do. Even the examples you list are conditional. Shepard romancing one of those characters will obviously end that pairing. EDI/Joker and James/Ashley are "vetted" by the player, meaning that Shepard has to show approval in order for that to proceed. Javik/Shepard isn't treated seriously in the slightest and Shep's shown to be horrified about it the next morning. And both Javik/Shepard and James/Ashley are treated as casual hookups with no subsequent mention, though Tali/Garrus and EDI/Joker are implied to be more serious.
Idk. I just don't see her as being cripplingly lonely. An introvert, yes, but not a hardcore loner.