Does a history of social anxiety significantly damage commercial pilot career prospects?
I don't know about the question in your title, but I can answer the question in the body:


  I was wondering if it's important that I disclose this to employers or just lie if asked?


No, you should not lie about your medical history. If you knowingly lie about your medical history, and it subsequently comes out, it could cost you your career - including the tens of thousands of pounds (or euros or dollars) you spent on getting your CPL or ATPL. Even if you have insurance against losing your medical certificate, they almost certainly won't pay out in this case, leaving you with a debt bigger than a student loan and no job to pay it off. It'll also make it much harder to get a medical certificate in future and return to flying status.

Worse yet, if the reason this comes out is because of an accident, you may face a criminal investigation because you flew knowing that your medical certificate was not valid, regardless of whether you think your condition could have contributed. You can't expect your employer (ex-employer) to stand up for you in this case.

Although I have a class 2 medical in the UK, I'm no expert in the medical requirements. It would surprise me if a past mental health condition which doesn't really affect your ability to fly, and which was successfully treated without medication, would stop you getting even a class 1 medical. It would probably just mean more uncomfortable questions in the medical exam, and probably having to get a written opinion from the psychiatrist who treated you. That might cost you some time and cash in the short term, but it's worth it to know it won't come back to haunt you later.