It's a public building with a lobby which is fully accessible by the public. It's not his space and you don't need his permission to enter it, nor do you need a cover story to explain your reasons for being there. It seems positive to me that you have thought of doing something which could help your anxiety, it shows agency and self-management. It would be different if you were planning on sitting outside his room staring at the door, but you aren't. I feel a bit sad for you that you haven't been fully supported in the strategy.