I agree with most of the above. The Extended versions of all of the LOTR films have none of the newer protections (Sony ARccOS, or RCE, etc.) I was able to rip all of these using DVDShrink. I also know others had no problems using DVDDecrypter, to rip all files to their hard drive in file mode. Default settings, and last versions, in both cases.
Clean the disc.
Try a different burner, as some will choke more often on dirt, scratches, etc.