Check our Big Blue TL3500Supreme. It for sure wont hold the 3500 lumens for 3 hrs, but I tend to run it on the middle settings anyways.
They're now called 3800 lumens, so let's do some math.
Battery is 4x 18650's, optimistically that's 3.6v*3.5ah*4cells=50.4wh battery pack and we will be generous and say that it's 90% usable which is 45wh available.
Big Blue claims 3 hour burn time which from history we know is something they don't lie about because their customers can measure that.
3 hour burn with 45wh battery means an average of 15w consumption.
Best emitters out there are going to be about 170 lumen/watt, and they aren't using those emitters, but we will assume they are because they seem to think their lights are full of magic.
170*15=2550 lumens average during the 3 hour burn time. But wait, their literature says it's 3800 lumen for 3 hours, how is this possible? Guess what, it's not, they have lied about the output of every light they have ever made, as well as selling canisters that were allegedly un38.3 compatible but still exploded and almost killed a diver, so there's that.
Now that 2550 lumens is assuming 100% efficiency, using the highest quality emitters possible. The reality is that they're probably using emitters at around 110lumen/watt and the optics are only about 80% efficient at best, so 110*15*.8=1320 lumen average which holds true with the testing that has been done about their output which look like this.
Compare that to the Dive Rite LX20 which has a constant output driver and I'll take the one that says it's an 1100 lumen light and puts out 1000 lumen, vs the 4000 lumen light that only puts out 1100 lumen after 30 minutes.