Faulty Window Regulator?

There is a spring in the regulator that should keep the window up. use a compact miror and inspect the backside of the regulator and see if the spring is still intact

On a related note, what type of grease is best for the rollers and tracks? White lithium? I need to clean and lube mine while I still have the inner door panels off.

It's actually the spring inside the crank assembly that's broken, you can't see it unless you drill out the rivets holding it to the regulator"scissors".
My 67 did the same thing, difficult to crank up or down and would "fall" down from fully closed.
Two ways to deal with this. First and likely best, places like NPD will sell you an entire new regulator assembly. Don't get just the "scissors" they sell. Though nice, they won't help.
Second, do like I did and just replace the crank assembly. I discovered the crank assembly from a 79-93 Mustang is all but identical. Thes Fox Mustangs have very different window setups though, so you can't use the rest of it. Junkyards are unfortunately only interested in selling the assembly, not just the actual crank part. Happily no one ever seems to want such regulators so they can be had pretty cheap. But being so different they hardly wear the regulator at all, unlike our old heavy windows.
I drilled out the three rivets holding the cranks on and just fastened the Fox Mustang crank to my regulator. After much cleaning, lubing, and some new bushings, my regulators crank the windows up and down with just two fingers and stay wherever I set them too. Worked out so well I did the driver's side too.
Ford has always called for white lithium grease for lube . I haven't found anything better.