If I can add since I did exactly the same thing. Go to iTunes prefs, Advanced tab, click on iTunes Music folder location options to change to external HDD. Then go to iTunes main menu, Advanced->Consolidate Library & that will copy all songs over to the new iTunes music library on the external HDD.
In order to copy songs to iTunes from LW, you should enable (turn on/mount) the external drive before you open LW.
BTW when I moved my iTunes library off my comp it was around 55-60 GB in size, now it's around 95 GB.
And "don't" fill your external drive more than about 75% full or else you will notice a dramatic change in reliability & speed!!!!!!