Sorry, Stijnb, but there is ABSOLUTELY AND COMPLETELY no possibility of a raspbian system working at all -- not even a little bit, not anything, no login, no init, nothing -- without the
/lib folder. It is exactly as feasible as someone saying, "I was driving my car and someone said to look for the wheels, but I looked and there are no wheels!" If you got in the car and managed to drive it, IT HAS WHEELS. Period. End of story.
So you are somehow mistaken. Add the output of
ls -l / to your post if possible.
I doubt very much any of the tutorial information you have read has instructed you to replace
/lib, either. That would be (again, pure and simple) malicious, since the most basic and essential components of the system, beyond the kernel, are in
/lib. There is no possible reason for replacing the whole directory. Most likely you were to add a directory for your new kernel to
/lib/modules, or replace an existing one. If it is the latter, move the old folder to somewhere you can get it back from again (e.g., just rename it). The
/lib/modules subdirectories contain kernel modules such as hardware drivers.
Whatever you've done, if you've removed stuff willy-nilly from
/lib and now have serious problems, you're screwed (unless of course you have a previous backup) -- you might as well just start from scratch with a fresh image on the card.