I did something similar to what you are trying to do. However, I used a ACT ZTW103 instead of an AS101. The ACT ZTW103 has been replaced by the LTM-5.
In my case, the ZTW103 transmitted a Z-wave signal to control the LFM-20. To make it work, I converted the “load” wire that connected the original switch to the original lamp fixture into a neutral wire. I clearly the ends new “neutral” with white tape to indicate that I had made a change. Using the new neutral and the line wire that was already in the box, I was able to power the ZTW103 and use it to control the LFM-20 using a Z-wave signal.
What you are proposing is hard wire the AS101 to the LFM-20. It is a clever idea and it just might work. You would convert the existing “load” wire between the existing wall box and light fixture to a “yellow” (signal) wire and use the “line” wire already in the original wall switch box to provide power to the AS101. This should work because the AS101 can use either neutral or line to connect to the "White wire w/ Red Strip. Once you have hooked up the AS101, you can control the LFM-20 with a direct Z-wave signal or via a Z-wave signal to the AS101. As long as you know how to safely do electrical wiring, it should be an interesting project. Another task you will need to perform before you can install the switches is to figure out how to mount LFM-20 in your ceiling fixture. Since you appear to be using fluorescent tube lighting, you should have enough room, but make sure that you do. When I did my LFM-20 installation, I converted my light fixture from fluorescent to LED lamps, so I needed to remove the fluorescent ballast. This added another level of complexity to my LFM-20 installation.
I used the ZTW103/LFM-20 combination for several months, but I did not find the ZTW103 to be reliable enough when it came to turning my ceiling fixture on and off. It took some effort, but I was finally able to pull a neutral from the ceiling fixture to the wall switch box. I then installed a Leviton VRS-15 switch and I have been very pleased with the results.
The fact that you will have a hard wire connection between the LFM-20 and the AS101 , should give you a much more reliable switching circuit than I had with the ZTW103 / LFM-20 combination.
Pleas note that your LFM-20 wiring diagram may not be correct. If you connect blue wires on either side of the load as show in many LFM-20 wiring diagrams, the circuit will not work because you will not have an AC power source for the lamp. Instead one blue wire needs to be connected to the power source that you will use to power the lamp (24 to 277 volts AC). The other blue wire should be connected to the lamp as a “load” wire. Then you will need to connect a neutral wire other side of the lamp. I contacted the Evolve engineering team regarding this error. They acknowledged there was a mistake, but they do not appear to have corrected it. The wiring diagram for the ZRW103 (LRM-AS) presents a more accurate picture of what you will need to do. The only difference is that you need to remember to connect the extra blue wire of the LFM-20 to the AC power source you want to use.
Under no circumstances should you connect the two blue wires, especially if one of them is connected to power.
Good luck with your project. My personal preference would be to try to pull a neutral wire and install a Leviton switch or dimmer that used a neutral wire. However, if that is not possible, using the AS101 and an isolated relay (LFM-20) in the overhead light fixture should work if it is wired correctly.