A 77" diagonal image is 1.6425257 square meters in size. Lux is measured in square meters and lumens are measured in square feet, so you have to do some size conversions.
So, going here:
Lux (lx) to lumens (lm) conversion calculator and how to calculate.
www.rapidtables.com
Put your brightness in (in lux), use the drop down to select that your measurement is square meters (as is standard for lux measurements) and put your screen size in (1.6425257) the surface area box, then hit calculate.
Just over 1,300 lumens.
Yes, the HDR color filter takes away some brightness. This is pretty well established. It is because projectors generally suck at HDR content and don't process HDR properly and never will until 10,000 or 20,000+ lumens is normal in the home on a 120" diagonal. Granted a miniscule 77" size is far smaller than what anyone uses in home theater, so I hope that was just for testing.
At the end of the day, Sony projectors are well known to be dim. I find this to be problematic with their products and one of the reasons I think that JVC is almost always the way to go. The Sony models still look really good, but they do tend to try to aim for a 100" diagonal maybe 120", but not a 133"+ sized image.
Anyway, I don't know about what all tweaks you have been playing with, and I am next to positive that you aren't doing any damage to the lamp. Running a lamp in high brightness does shorten lamp life, but that's consistent with all projectors. Likewise, I'm not sure how many hours are on the lamp, so, more life used will mean a dimmer lamp.
At the end of the day, LUX is meaningless on projectors because it is FULLY dependent on screen size. Any projector review that talks about LUX is providing just crap information. Useless. You have to work through all this math to get back to the actual brightness in foot lumens, and it sucks to do. But, if you are measuring things yourself, LUX is the common way for many devices to take measurements, so you measure in LUX, then convert to lumens. Just know your screen size and ensure you are putting in the proper numbers.