During playthroughs of the trilogy where I don't romance her. I like to think this is who she ended up with after the Reapers are defeated. I remember a quote in the Citadel DLC where he says Protheans actually did date the Asari back in their cycle. And during the goodbye scene on Earth where he says after the war is over, he may consider writing a book about the Protheans with Liara (Don't let him use that Echo Shard) So I think I reckon it is feasible that they eventually became close.