The behaviour you're reporting is incorrect. I'm running the same config and hardware as you and LB is available in all Spaces/desktops, including full screens.
[Re: assigning apps to desktops, that feature is still available (except where the app you are selecting is in full screen). Easiest way to do it is to click and hold, or ctrl-click, on the app's dock icon, and select "options" "assign to" in the pop-up menu. But as far as fixing your LB experience that's not likely to be a fruitful avenue anyway]
Note that depending on how you are set up, you will have to invoke LB separately in each space/desktop; it will not stay at the front across desktops.
Action: Repair permissions, restart your Mac, download the latest LB nightly build and install, repair permissions, restart. Now that might seem like a pain, but you will know you have done everything right as far as LB is concerned, and we can more readily solve any real underlying problem.
[Re: assigning apps to desktops, that feature is still available (except where the app you are selecting is in full screen). Easiest way to do it is to click and hold, or ctrl-click, on the app's dock icon, and select "options" "assign to" in the pop-up menu. But as far as fixing your LB experience that's not likely to be a fruitful avenue anyway]
Note that depending on how you are set up, you will have to invoke LB separately in each space/desktop; it will not stay at the front across desktops.
Action: Repair permissions, restart your Mac, download the latest LB nightly build and install, repair permissions, restart. Now that might seem like a pain, but you will know you have done everything right as far as LB is concerned, and we can more readily solve any real underlying problem.