I know how to install a LUKS/LVM Ubuntu system using the alternative CD. Is it possible to do this with an already installed normal system? Meaning that I have an unecrypted system now and don't want to do a reinstall for LUKS/LVM.
No, you have to re-install as a part of encryption (LUKS) writes random data to the hard drive over writing your data. You will have to back up your data an re-install.