Desktop folder is not a great place to download to anyways. Connect & turn on your external drive first. Then open LW. Then go to LW's menu bar, Tools -> Options -> Transfers, click Browse button & choose your external drive.
LW has never been great with external drives. However LW may have improved with the later versions of LW 5. The issues involved are:
(a) External drives tend to go to sleep. (b) If the external drive is not turned on or is not active (asleep) at time of opening LW, LW will not see it & revert to the default location in your personal account folder. (c) If using a USB external drive, best not to have many if any other usb devices operating from same computer usb port.
BTW wherever your download folder is, your incomplete folder will follow beside it.
(Click attachment below to see larger view of sample settings in LW's options window.)