I've no idea, but I wanted to say kudos to you for trying and looking for help. My socially awkward ass would probably chalk it up to a loss and never initiate with the guy again.

About the only thing I can offer is I've sort of been that guy. Had a friend who would have game nights every so often where he'd invite a bunch of people over. I'd almost never go or respond, but damn if I didn't appreciate the hell out of always getting the invite.

Maybe he thinks you want to get him in the sack? I'd be more clear about the wanting to grow a friend group and see if that does anything.

It might be the activity. I personally cannot stand going to restaurants as an outing. I would find a common interest and invite him to an activity related to that.

Usually I stop after 2 or 3 attempts.

You could also ask him directly. Maybe he's generally not interested in lunching together, or he was just too busy to respond, or whatever. These questions can be awkward, but also deepen a friendship. A risk-reward mechanic in the game of life.

My gut reaction (that others seem to share) is that the activity might be the problem. I always hate giving up my lunch during the workweek, because it's my only alone time to unwind during the day.

Try a different activity (group activities can be less intimidating for sure, like "hey I'm meeting a few friends at a park Saturday if you feel like swinging by" because then there's less pressure on them specifically). Maybe a walk or something on Sunday mornings, or ask him about his hobbies specifically? You can also just communicate via phone and still be friends. Maybe he's still just working up to the point where he feels comfortable hanging out socially frequently.

Good luck!

I feel like three is the magic number. Any more than that and it seems too persistent.

Maybe wait a bit and suggest another activity?

I echo the sentiment about the guy possibly not being into the restaurant scene. I'm 39 soon and feel ya completely. It's a tough time at this age finding meaningful friendships.

my younger brother is like this lol. we have a really good relationship, but he's a busy person and sometimes a text message, even an invitation to something, will go completely unanswered, but we'll have an entire conversation in the same thread the following day.

sometimes I'll send him a text that is an invitation, and part of a different conversation, and sometimes he just responds to the conversation part and completely ignores the invitation side. I'm not entirely sure what's going on there, but it's not unusual.

try inviting him to something different. bowling maybe