Definitely leave the profile up there. I think it never does any harm to put yourself out there and you never know wht might happen. For me personally the online method, I don't think, would work but I know a few people who've met the loves of their lives that way. The right person is out there waiting or looking as we speak.
I think it's so exciting that you met someone for lunch. Take it slowly and let things happen naturally. I think there's sometimes a tendency to jump into things quickly when an LTR ends, but I don't think that's going to happen with you somehow.
