I'm used to working in the LAMP environment where it's just copying the needed files
You can still copy the files over. However, I prefer to use source control to sync up the files instead of using scp/ftp, etc.
and I've been doing the same thing in the same fashion - except instead of files it's functions being transfered via swank...
Assuming that you are using asdf for your project, you can just type ,load-system in slime REPL to reload your modified files.
I usually have gnu screen running and dedicate one terminal for my lisp's REPL (not slime).
When I need slime (for debugging), I just type (swank:CREATE-SERVER) and then I can connect from emacs.
HTH, -- Mac