I've encountered this problem myself and there is an easy workaround.
Thanks Helment, Just tried your solution above and it works!
That might possibly be the best first post ever here! Should the solution above become a "Sticky"?
Here is a short version of what your instructions accomplish.
First rename and hide the large logic sound "Library" folder on your external drive.
On your 2nd computer let logic download a tiny chunk of the "Library" to your system drive,
then tell Logic to move it to your external drive, quit Logic and replace tiny "Library" with your large one.
I also tried the inevitable - opening Logic without the external drive connected.
You will get a "... Library could not be found" message with 3 options. Just don't
press the 'Reset' option unless you want to reset where logic is looking for its Library (back to the default location).