I can relate to the guy problems. I've never been able to hold onto a guy friendship long-term even. Guys are just hard to understand because they seem to operate differently than girls. Believe me, plenty of guys have made me feel crappy about myself. I've avoided going specific places just so I wouldn't see the ones that hurt me. You're right that it's easier if you see less of a person so you can move on. So, if not going to lunch will help you out for now, then do it. There's no shame in that. If you're not comfortable, you don't need to put yourself in that kind of situation. You have the power to choose what feels right to you. Robby has no say in how you deal with the breakup.
On a side note, I know you're on the young side, but have you ever considered trying antidepressants? They won't get rid of the depression, but they can help ease some of the symptoms you're feeling so life might be more bearable for you. Also, have you thought about seeing a therapist? It's nice to have that extra support in your life that won't judge what you say and will be unbiased since they haven't known you your whole life. It's a safe place to talk about what's going on with you and trying to make sense of it. It's worth investigating if you haven't all ready. You don't want to keep suffering in silence because that won't make you feel better due to bottling up your feelings, so it's good to keep your options open just in case.