The latter

I honestly can't remember the last time I felt no pain, or didn't have random terrible memories crop up at 3 in the morning...I move on but with the pain and memories still inside me, lessons for next time and whatnot

Move on, although I have no idea what a break up feels like as a grown adult. I don’t count anything before my mid 20s as “adult”.

Transmute the pain and learn the lesson then move on they’ll probably be back

I'm always thinking about sex so I don't actually believe in love.

You learn how to live with the pain. You never really move on and forget.

I just move on. Might be sad for a day or two, but I recover. I haven't yet lost anyone so load-bearing that it traumatizes me for the rest of my life, and I'm not sure whether such a person exists.

I haven't experienced that yet but I don't think I'd be too affected.

i can't say i've ever really lost a love yet, though it's inevitably going to happen.
I don't think I'd choose to live with pain if i could help it. so i guess the answer is that i'd move on if that's actually possible, but it doesn't seem at all that that would necessarily be possible.
on the other hand, you did say memories, too...i'm not sure i'd want to erase the memories. or even ignore them. it's hard to tell.

Depends how I miss them.