Auto-indenting lisp expressions in Emacs

How can I get Emacs to properly auto-indent Lisp expressions typed into any buffer? My idea was that I open SLIME in a buffer, then a new file in another buffer and I write code in that another buffer and compile it and use SLIME buffer as REPL. But while there is good auto-indenting in SLIME buffer (with slime-mode), I can't get the same auto-indenting functionality in the other buffer.

OK I got this one: M-x lisp-interaction-mode and M-x auto-indent-mode.
I think I will bind these to a key.

Thanks for helping