If I move them in the next week or so should I put a lamp out there?
By lamp you mean a heat lamp, right? If the coop is big enough, so the lamp does not make the whole space too hot, that would be the easiest thing. Just be sure it is safely secured so you don't start a fire, and put it in one corner so they have lots of space to get away from the heat. Check them after dark and again first thing in the morning, and if they are all sleeping away from the heat you can remove it.
when is a good time to move them outside at this time of year? I live in East Tennessee and right not the temp has been been mid 40’s/low 50’s to mid 70’s/low 80’s.
It often works well to brood chicks in the coop from their very first day, so yours are definitely old enough.
At their age, and with those outdoor temperatures, they should not need heat during the day. They might need heat at night for another week or so, or they might be fine without it already.
In the photo, it looks like you might have a red heat lamp bulb. Usually, the first step is the remove their heat source while they are still in the brooder and see if they are fine without it, then a few days later move them outside. Or it works equally well to move the heat source outside with them, and then remove it when you see they no longer need it.
Whether they are in a brooder indoors, or out in the coop, it is always important to have a cool area where they can get away from the heat. That prevents overheating, and lets them adjust to cooler temperatures at their own pace. It also makes your life easier, because you don't have to be picky about the exact temperature in the brooder. As long as one corner is warm enough, and a large area is cool, chicks do very well at moving around to regulate their own temperature.
These little boogers are currently in a 4x8 brooder with 18” walls. If I didn’t have the hardware cloth on the top they would be out! They’re constantly running, “flying”, and play fighting. I think they have plenty of room now (13 birds in a 4x8) but the coop and run is going to be so much bigger. I feel like they’d love to be out there, given how active they are.
Yes, they would love to have more space. The sooner you move them out, the happier they will be.