Welcome to the forum! Hopefully others with more expertise will chime in. But personally, I wouldn't have expected the imperfect THD to result in flickering lights. Was the generator putting out the proper voltage and frequency (60 Hz)? My "normal" (contractor-style) generator was a Generac, nothing special, and I don't recall ever having issues with flickering lights (I had a lot of fluorescents, and I think some LEDs at the time).
I would expect the THD to have more of an impact on sensitive devices. But the LEDs need to take the AC and convert it down to DC, perhaps the dirty power was somehow causing trouble with that process.
What's your budget? And how much power do you need? There aren't as many choices once you get up to the 50A-output range. The Hondas have an excellent reputation for quality, noise, and electrical output, but they're priced accordingly. This one is 6500W max, 5500W continuous, and lists for $2,200:
I'm impressed that the Firman actually lists a THD spec, that's not something that I'm used to seeing. I wouldn't count on finding it for most generators.
The cleanest electrical output will be from a good inverter-style generator. Those create DC, and use a pure sine-wave inverter to make clean AC from that. They will have a much lower THD, and they can change their RPM based on the electrical load (since the output power frequency is not tied to the engine speed). This makes them quieter (they can just idle when powering a smaller load), and also much more fuel-efficient. Which is cheaper to run, but can also be a big help when fuel is tough to get.
This 3300W Firman inverter shows 3% THD, for comparison:
Their downsides are cost, and output. They're considerably more expensive per-watt, and there are not many that output 240V, which is what you'd want, for tying it into your house.
This Briggs is an impressive value, for inverter generators. I don't know how good it actually is, but it's 5000W continuous, 6500W starting watts, for $999. And it outputs 240V.
This Champion inverter is even cheaper, at $699, and 5000W/6250W, still providing 240V output:
That type might be your best bet for low THD, and still a decent power output. But I don't know what kind of loads you need to run. I suspect you will have a hard time finding a very-low THD, and ~8000W 240V output, in the $800 range of what might be a similar unit to your Firman:
I am using an inverter generator now (Honda EU2000i), and really like it. It's only 2000W max output, but it just purrs quietly, typically runs my loads for 6-7 hours per gallon, and provides very-clean output, which is nice for peace-of-mind with appliances, etc. I've added a second one in parallel for 4000W-max. A single larger unit would make more sense for most applications, though (I originally bought mine for a different, portable-use purpose).