LR doesn't know it's your backup drive, to LR it is just another drive attached to the system therefore a possible source for pictures.
I should have said that it has just started acting this way after working "normally" for a long time. That is, the back up drive acted as a backup, and didn't cause LR to turn on and look for pictures to import. LR only did that when a plugged a memory card into the computer.
Have you put it into a different USB port than usual? it could be the autoplay settings.
You can check by right clicking the start button, click control panel then double clicking Default Programs then choosing auto play settings, the option will be under removable drives, alter it to whatever suits your needs.
Thanks - I confirmed the auto-play settings for a removable drive, and that seems to have fixed it and I can LR still starts so that I can download new pictures from a memory card.
Not sure why things changed, but thanks for helping me fix it.
You're welcome, glad you got it sorted.