We have an S-tube trap (pvc) similar to a P-trap that keeps a water barrier. No insects or lizards yet 12 years

A P-trap would not have prevented the problem that the OP described. If there is blockage in any part of the drain line, the condensate pipe and drain pan can fill with water and cause the HVAC unit to shut off.

His son had a lizard crawl up and die blocking water flow then and vacuumed drain out.. With proper maintenance annual/semi-annual treatments vinegar or chlorine water mixture should eliminate algae from forming a screen will not prevent this only ingress of bugs/lizards. A water trap will do the same.

I agree. But, if the P-trap is located near the inside HVAC unit, you may have about 20 feet or so of empty pipe for animals to clog up the pipe. I don't have a P-trap or a screen, and I have never had a clogged drain. But, I do keep it flushed out.

It's similar to a p-trap made out of 3 elbows and and 3 pieces of plastic tubing

Stay away from using Bleach in your drain line. Over time, it can deteriorate the glue that holds the PVC pipe together.

Note that the plumbing code requires all drain lines that are connected to the sanitary sewer system to have a P-trap installed on them. This is primarily to prevent sewer gas from entering your house, and it does provide some protection against insects and small animals. But the condensate drain line from your HVAC unit is not required to have a P-trap. Personally, I would not want a P-trap on my condensate drain because I think it would be more likely to cause a clog than to prevent one. Most clogged drain issues in a house are caused by a stopped-up P-trap.

Found these interesting tidbits:

Do I/you need a condensate drain trap if you have a condensate pump?
Yes, you need a condensate drain trap, even if you have a condensate pump. To repeat, the purpose of the condensate drain trap is usually to stop conditioned air from being blown outside. And this same logic applies if you have a condensate pump. However, without a trap, you will blow conditioned air into the pump, usually in the crawlspace, basement, or attic.

Are condensate drain traps required?
No code requires a condensate trap. However, IRC 1401.1 (we use the IRC here in Virginia) requires following the manufacturer’s instructions for installing “heating and cooling equipment and appliances.” You will be hard-pressed to find an AC installation manual that does not require condensate drain traps. Below is a diagram from a Carrier AC installation manual as an example. Notice that it requires installing a trap on both condensate drain lines.

Checked the manual from our just installed Carrier system and it does "require" one.

Copied from here: Your Air Conditioner Needs a Condensate Trap

. Won't those screens have more chance of getting clogged from the crud that often is drawn into the line from the condensate tray? Very often those lines get blocked, but not with animals. When they get blown out a lot "lint like" crud comes out.

My Carrier HVAC system was installed by The Villages builder and it does not have a trap on the condensate drain line.

However, I did have a Carrier system in Virginia, and it had a trap on the condensate drain.

I would be more concerned that the crud would clog up the condensate trap, if I had one. I think the loss of conditioned air is minimal. Personally, I don't plan to install either a condensate trap or a screen on the end of the pipe. As long as the drain continues to flow, I am happy.

My condensate line is one big trap. The line goes straight down from the unit, through the wall, then back up on the outside. Of course, the outside portion does not rise as high as the unit itself. Under normal conditions most of the line is full of water.

A short trap of some sort might help with the anoles. My line was blocked by one. The Amazon screen or even something simpler should also work for this particular problem.

Note that, if your condensate drain is already trapped, adding another trap could result in double trapping.

"Double trapping causes drainage issues because air becomes trapped between the two traps, and air is lighter than water. That causes the air to travel up as the water flows down, resulting in no drainage."

You probably should check. In the past some have recommended vinegar, a mild acid and others bleach. Today they say plain water. I do ours once a month with plain water. So far 9years, no problem

Bleach *may* have an effect on the PVC and connections. Fumes from the vinegar or other acid *may* come back up the line and affect the aluminum condenser. It is probably debatable how significant either of those two concerns are but it's hard to imagine they would be recommended at all if they were high risk.

We use a gallon of hot tap water every month. No fumes and no mixing/measuring/dilution required. The volume *might* be enough to flush the lines and the temperature *might* be enough to kill any algae. If the gallon begins to back up then I know I have a problem starting and can take other measures to clean it out (nothing so far). I don't have nine years with this technique yet but so far so good.