I am wondering how AZ law works in regards to new vehicle lemon law. Does the satisfaction have to be to the customer and not to the manufacturer or dealer, and does it have to be a major issue?

I have a new 2020 F150 with 800 miles that is making a popping and clunking sound in the rear. I think it is the rear leaf springs and Ford is going to replace those for me, but I am just kinda wondering what next if that doesn't solve the issue. I have also read where the manufacturer has 4 attempts to repair the same issue before the lemon law kicks in.

Has anyone here ever had to deal with this.

I did back in 2003 with a GM product.  Back then it was 3 attempts to fix the same problem or 30 days in the shop in a year, mine sat 34 days in the first year.  I believe i contacted the BBB and they helped get the party started.  Was actually a fairly easy process, they have a formula for the refund was price paid minus a fixed rate for the miles.  

GM offered me a 100k warranty or buy back.  I took my money and went to Ford, after owning a couple Ford’s now I buy Toyota.

I’ve looked into it. I bought a new 19’ ranger lariat loaded. The modem for the ford pass app and everything associated with it hasn’t worked in over a year. Been to the dealership 4-5 times and they can’t fix it. Last communication was that it’s a known problem and ford has no solution.  Arizona law states 4 attempts to fix the same problem is a lemon and a lawyer can file with no cost to
You. Ford will have to pay all Lawyer fees as well. I financed through ford credit at 0% so I’m contacting ford customer care first this week to see how they handle it. I don’t want to have any possible blow back if I go directly to a lawyer. I’ll update when I here back from ford, but if I’m not impressed with the compromise, the lawyers will then take over.

Some people have said that the BBB was helpful and worked on their behalf to file a claim. I also understand that the vehicle needs to be of diminished value to the customer and corrected to their satisfaction and not Fords.

Don't mention anything about a lawyer to Ford. They will treat you completely different once you do.

If you are unhappy with your progress, get the lawyer and go from there. At this point your lawyer will handle all interactions with Ford. (Which is exactly what you already posted)

IANAL