I recovered the data from a MBL for a friend a few weeks back. I used an external USB 3.0 dock, estata would have been better, and a free product called R-Linux, which runs on Linux or Windows. I used the Windows version because that was where I had USB 3.0.
The product scans the disk for files and then shows them to you and you can select which ones to recover. The process took a little over 60 hours for a 2TB MBL and required intervention several times because the software kept trying to read places on the disk that were not recoverable and I had to manually pause and restart the disk scan to get it to continue.
Hopefully there is a setting, that I overlooked, that can cause it to move on after so many tries. In my friends case a lighting strike took out several consumer electronics devices in spite of protection, but the actual hard drive was damage in a couple of small areas that refused to read and he only lost 12 files, all of which were replaceable music files, he was very lucky. It could have been a total loss if the drive would no longer spin up, or an important file had been destroyed without another backup.
This event compelled me to get all of my pictures and music onto three different NAS devices in addition to the original copies. The original copies are not safe and they are not organized, so recovering from those would be painful as well if one can find them.
The thread that helped me on this forum, and why I now have my own MBL is this one:
http://community.wd.com/t5/My-Book-Live/Data-recover-on-a-My-Book-Live-2TB-HELP/td-p/430120
Hopefully in your case you can just read the data directly from or Ubuntu or use something like Linux Reader mentioned in the linked thread. R-Linux works great, but requires attention to see that the disk scan has not stalled, but can recover disk with nasty issues as long as they still spin up and the heads are not damaged.