I have never used Lee's tumble Lube but from what I can see on YouTube, it's a liquid. I can't see how that would work with a Star sizer. You would have lube all over the place.
However, I'm pretty sure that you could tumble lube your bullets in the conventional manner and then run them through the Star sizer. I just don't know if that would leave enough of the lube on the bullet after sizing.
I think Lee has a push through sizer that you can use with tumble lubed bullets. It mounts on a single station press.