I am using an Apollo e7000 spray gun system that I bought new and Valspar pre catalyzed lacquer, following all manufacturers guidelines, in a well ventilated, dust free spray booth and I'm getting particles in my finish. It looks like large particles that are atomized from the finish itself and not dust. What is going on?

Here's another photo of the issue

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use a fine mesh cone filter.

a number of things can cause there to be junk in your finish;
dust blowing around in the booth
clean the booth
junk in your finish
stain your finish
dried finish in your pot, gun, lines that gets softened up when you refill
clean your delivery equipment well and install filters
sanding too soon after a coat. instead of powdering up your soft finish balls up and sticks to your finish ...even compressed air dusting and tack ragging can leave this residue behind
wait before sanding
All that said...l have a enclosed booth, I clean it every day, l strain my finish, l clean my equipment well, l filter all my finishes between the container and the nozzle, l wait before sanding and then l blow off or vacuum the sanding dust and then l tack each piece just prior to finishing it and l still get a bit of stuff in my finish

That's pretty big.
Perhaps:
1. Stuff floating around in your booth.
2. Something from you, your clothes, hat, etc.
3. Stuff coming off of your hose.

Generally speaking, for Dust/Junk/Dirt removal, sweeping and vacuuming works better than blowing.
good luck

Looks like junk in the finish. We've seen that before. The only quick remedy was if we could quickly use a fine pair of tweezers to pick it out immediately. Then, the surrounding finish will flow and smooth the surface. After a minute or so, this doesn't seem to work. But that is not a proper solution. Nick had some good thoughts. Here is our experience.

We used a good cone filter with a gravity feed cup gun for a long time. The finish material was filtered well as it was poured into the cup, but we still had the same problem as shown in the photo.

It turns out that finish was getting on the screw top threads on the cup, drying, then falling into the previously filtered finish. We learned to clean the cup and lid extremely well.

Another spot that caused problems was build-up of a bit of dried finish on the tip of the gun. This was with a water-borne product. The solution was to keep an eye on the tip. If there was any dried build-up, which would eventually break off and fall onto the work-piece, we simply broke it off with a fingernail. Sometimes this had to be done a number of times during a single spraying session. We learned to simply look at the tip. One clue that the tip was having a problem was that the spray pattern changed. Either the pattern changed shape or the amount of finish decreased. Problem: dried finish on tip. Solution: break it off with fingernail before it hardened.

We have just switched to a pressure pot system (from the gravity feed gun) and just completed our first water-borne project. We did not have this issue with the solvent-borne projects. Yes, we have a different pressure pot for solvent and water. I did see some build up on the tip after the gun set over night. It appears that some of the water-borne finish cured just inside the nozzle. We are learning how to care for our new system and hopefully we can avoid this issue with our water-borne setup.

Catalyzed and pre cat products can get a jelled, partly cured skin develop in the pail, cup or whatever you are using. These things can squeeze through a filter and through the tip. Especially an HVLP. I could be wrong but a thorough house cleaning in particular the equipment is needed.

Seen this many times with HVLP rigs.
This may be "snot" building up at the tip of your spray gun, due to warm air created by turbine.
If you are spraying for long periods of time, stop every so often and clean any debris from the gun tip...
My 2 cents worth... Good Luck!