Davel didn't like it.
Yes, Davel didn't like it when Lycia didn't even say anything about his invitation, and he also didn't like the way Shirley suddenly dragged him out of the meeting room when he was about to ask Lycia why the doctor wanted to stay in the meeting room with a guy named Nick instead of following him into his office.
Before Lycia could respond to his invitation, Davel had to leave the girl, and now he didn't know if she wanted to have lunch with him or not. How was he supposed to know? Even when he was still a spiritual being in his world, he didn't have the ability to read a person's heart, and that was why he couldn't guess whether Lycia would say yes or no to his invitation.