Can I register domain names with only one character?

Yes you can. This character can be a letter a-z or a number 0-9.

Update, December 15, 2011
NIC.LY has announced that all future registrations of .LY domains that are shorter than 4 characters are only allowed for companies or individuals having presence in Libya.

All currently registered domains that are shorter than 4 characters, can be renewed normally.
We advise all clients to renew their domains before the expiry date.