It seems to me that the LW here has created a problem of appearances where none previously existed. She had no obligation to give the boyfriend the information he asked about, but she could have given him a non-response that was not untruthful. Now she's lied, and if the BF learns that in fact her current adviser was her former lover, he's going to wonder why she lied. A sensitive BF would be generous and accept the explanation that she was shy about the relationship, but a suspicious one will wonder if she misled him because she still harbors feelings for her adviser.