(I give direct, no BS advice. It is nothing personal against you. Don't take it that way.)
Well, I have to dissect this in sections. Here goes.
Then a couple of times he seemed distant to me. So I suggested we take a step back. He says, he wants us to work out but his feelings for me aren't there right now. And if we take a break, then maybe they will come back.
Logically, he thinks the two of you can work out. But it takes more time for feelings to grow. That's all that is. Plus, if he takes a break, he believes his feelings will be in line with his logic, because he will miss you. If he misses you, that means you meant something to him. Sounds counter-intuitive, but it works.
Well, what can I say to that? I said I wanted to take a step back, too. The truth is I don't like him being distant. And if he is going to be distant, then maybe we should end it. We both deserve better.
Be patient. Feelings take time to grow. He is distant because you have been apart for a while, and his heart may be shy about you. To give up now is immature and simply gives him a reason to NOT see you. He doesn't want someone immature, impatient, and unwilling to wait.
So that was Monday. I am trying really hard to just use the time to decide what I want. He may or may not come back. We really didn't set any ground rules for the break. He asked me to schedule lunch for two weeks from now (when he returns from out of town) I think I was just being stubborn and didn't take him up on the invite.
Stubbornness=another sign of immaturity.
I actually feel like we are pretty close and can talk about very personal things. So I want to tell him I was stupid to not schedule the lunch. But I get that he can't miss me, if I don't go away. Should I reach out to him and schedule the lunch or just let it go???
If you really respect him, admit you were wrong (to him) and accept the lunch date. This is a case where "waffling" is acceptable: when you admit you were wrong and you really want to see him because YOU REALLY LIKE AND RESPECT HIM. Even though you agreed to no contact, this is a case where you need to make it clear you like him and want to see him.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
(Please note, we give the best advice we can based on the information given in a post. For better advice, please include the age of all romantic partners.)