Hi Ben,
I think that you are under no obligation to mention anything about your mental health issues on the site, actually. Not mentioning it does not make you a liar. What would you be 'lying' about??
Umm, nothing. An omission is not a lie!
I think that very personal, private information like that is something that you mention or reveal to someone once you have been on a few dates with them, once you get the feel of who they are as a person, and they you. You are not obliged to spill it all up front.
As far as the things you mention - like the restaurant and the tube, etc., those things can be easily worked around, without you having to go into full reasons why IMO. Like 'Well actually, I know a nice, quieter restaurant where we can have a good chat', etc.
It is a sad fact - even in the year 2014 - that any mention of mental health, and many people have a ridiculous image of padded cells and straightjackets, when in fact we are just ordinary people with ill health, just like a physical problem, that's all. For that reason, I would take your time to get the feel of someone, and then gently ease in to that conversation, when YOU feel comfortable, and the time is right.
I forgot to say - your mental health problems do not define you as a person. Yes, it is an element, but it is not your personality, your character and all the other things that make you who you are. The right person will see that!