If I remember right, Lucy was Raj’s first girlfriend on the show. And probably the first girlfriend ever for him, since he was so shy from the start. She was a memorable character, despite her massive flaw.
While she wasn’t mute around men, she was definitely more socially awkward and shy than Raj was. Where most social settings would have her show signs of PTSD.
While he was genuinely trying to help her, he went too quickly, too far and scared her away for good.
Lucy surprisingly shows back up near the end of the show when Raj arranges all of his ex girlfriends to get their feedback. And she tells him that awkward events causing social anxiety (like the one she’s attending) is the reason she broke up with him.