Hi!
I do have success using clay alternatives both with car soap or conventional clay lube.
If I'm going to clay (with towel, block or mitt) a wet car, I use shampoo diluted in a sprayer bottle.
If claying a dry car, I'll use clay lube.
Differences I've noted: clay alternatives do more marring when claying a dry car with clay lube. So in my opinion, they work better with car shampoo.
I've used both wash and wax or just wash shampoos and had great results with both.
However, it's always better to do a test spot and see if in your case you'll get marring with shampoo/lube, because softer paints may show marring more than harder paints.
For sure you should test both and see what you feel better working with. Final results will guide you through your best practice.
In my last details, I've chosen claying (clay block) with soap just after washing as my default practice, when I dry the car I have a clean and clayed car, so that worked fine for me. I pretend to use this sequence always as possible, as I believe I can improve time and even do a better clean/wash job claying with soap.
Again, you'll have to test yourself, but be fine because both will work great.
I've read somewhere that ONR (optimum no rinse) works wonders as clay lube with clay alternatives. In that case, I would make a '2 bucket' method using one bucket with ONR and another as rinse bucket (start claying ONLY AFTER thoroughly washing the vehicle first). Drop the towel in the ONR bucket, clay a panel and rinse in the rinse bucket. Or using a spray bottle, like I've said, it'll really depend on what you feel better doing.
Hope I've helped a little,
Kind Regards.