I'm also unclear about what she lied about. She told you she had an appointment, and you think she was with another client?

Maybe she considers all her client sessions as appointments (my T describes our sessions as appointments), so she needed to finish to get to her next client/ appointment.

Also have you considered that maybe she was having a supervision appointment. Therapists are supposed to have supervision appointments with other Ts. Maybe she has her supervision with another T working in the same office.