Eating together is also a bonding experience. So eating together can help foster trust. (Though I think this depends in part on the experience being a successful experience -- hating where the other person likes to eat might tell you there are potentially bigger problems in your future.)

Making your startup succeed requires you to have a lot of faith and dreams about your project, and a weekly lunch is probably a good environment for having this kind of team “bonding” around a common vision / dream.

It's not merely a good environment for bonding, sharing a meal actually causes some bonding all by itself, whether you discuss business or not. Humans are at their most vulnerable when eating and food sustains life itself. There are some very powerful psychological and emotional forces at work when you sit down and break bread with another person. It isn't merely "nice atmosphere".

I used to feed the single soldiers who came to my apartment in Germany to play role playing games with my husband. Every last one of them came to say "goodbye" to me when they got their orders to go back home to the US. And some of these strapping young soldiers cried as they hugged me goodbye, though their relationship had not really been to me, it had been to my husband. But I was the one who played hostess and cooked them Christmas dinner and put my kitchen at their disposal every weekend, not him.

Peace.

Same. I don't buy into the startup "lifestyle" of most B2C web companies. I'm pretty sure, in the US, it's a relic of the dotcom era that needs to die.