Fan and Light on two separate lines. Can I use LZW36?

Nope, only wall controls, I linked an amazon page with my exact current switch above.

Amazon.com

I was thinking that since you are going to be controlling the lamp via a scene you could just as easily use smart bulbs in lieu of a dimming relay in the box. Might be easier. The only problem would be is that you would have to run a constant hot to the fan light, which may not be a good idea as the only way to cut power to the light would be via the breaker.

Yeah Iā€™m not a huge fan of smart bulbs but I did consider that.