You'll have to replace the broken line. If you are that far in you might as well replace all the lines and cap tube to ensure there are no problems in the future.
How the hell do you do that? Lol...
Is this just a matter of purchasing new copper lines and just soldering them into place?
Oops! I'd tell you to replace the Old +60 year old Pig-iron/boat anchor of a compressor with a modern 1/4 HP unit & be done with it, but hey, you're almost halfway there already!
Your undoing was not removing the old steel line clamp on the side of the compressor, but I don't see why you started to separate the compressor from is mounts in the first place for just a rewire job. I suppose it's a lesson learned unfortunately.
My bro-in-law's handy work, not mine. He called me for help after the fact. So I have to act as a go between here. But it will be a good lesson and learning experience for me as well.