See my post in this forum - you can find it easily, of a few days ago - it's a related problem, also with a Laars Lite LLD (Propane - tho' the natural gas version has all the same components, with just a couple add-on parts different on the gas valve). I've reached a point by troubleshooting that I believe my issue is the valve itself. There is a way to test the gas pressure entering and exiting the valve - too complicated to explain here - and it does not appear to open although it does click when the HSI (Hot Surface Igniter - which is also the sensor for flame presence!) gets up to max temperature. I know this because after detaching it from the gas pipe I can see through the screen and when I reattach the wires and start the circulation pump and turn on the heater and the HSI glows and the valve clicks (you can feel the electronic "click" in your hand), I can see through the screen that the mechanical valve (the bottom half) does not open! So I've ordered a new Honeywell valve and this week I'll install it. I'm confident this will work. My point is you should troubleshoot this valve. My heater is 20 yrs old but the stamp on my valve says it was made in '97. So it was obviously replaced once before. I've had my heater for only 2 yrs and I've replaced MANY components. By the way, this valve is priced on various internet sites from $150 to $350! So shop around for any parts.
NOTE: Also, parts websites also show a "flame sensor rectification kit" - my model does not have this part. It turns out that Laars once had a problem on some sets of this model where the HSI was not sensing the flame, so they came up with this fix. Thus the name "rectification kit". Perhaps some problems could be related to this and you need that kit. (I eliminated that in my case by methodical troubleshooting.)
PS: I see many times people here don't post what their problem resolution was. That is not helpful to teach the rest of us!! Please tell us!!!!