Quoted: If you increase from say 65 to 105 or 120.   How much farther will it allow you to light up a target.

It will not double the range, though generally you can witness an approx. 20-30% increase in range with the P90 or P61 lamps over a P60.  The biggest differences with increased lumens are often the hotspot intensity & better, whiter flood.  Range often has to do more with the reflector format than the lumens rating.

Lumens is a measurement based upon light intensity at 1 foot distance, over a 1 square foot surface.

I think the question you are asking relates more to the "throw" distance of a light.

This  conforms to the "inverse-square" relationship, which means that  a light will be 1/4 as bright at twice the distance. This starts at the 2nd foot in distance when you are using lumens measurements.  So, when you are at about 50 meters, the intensity is only a very small fraction of what the lamp's rating is. When you get into real life situations with ambient light around and possibly smoke/fog, or whatever, the amount of useful added distance that you get from a light with double the power is actually quite small. You can also add the fact that the human eye perceives about a 3db change in intensity as the minimum needed for us to really notice a change in light intensity. You have to double the power to get a 3db increase in intensity, which is just about what we need to notice a change with our eyes. We can identify smaller changes(1.5db) but it is noticed as a very minor change which some may not even see at all when looking at a beam nearby. At a distance, it will help to put the beam just a little further, but not much. You might get 15-25 feet added useful distance.

The most effective thing to improve throw distance of a light, is to improve the optics/reflector system. Larger diameter reflector is better for this. But this makes the light harder to carry in your pocket. That's why most tactical lights limit the size of the reflector, to keep the overall size of the light fairly compact. Distance is all in the reflector, or optics/collimator.

The reasons why reflecting the light output works to extend the distance, is that the bulb outputs light in all directions, and we use only what comes out the front. When the reflector is good at re-directing the side output toward the front, we get more of the light to use the way we want to. The better the reflector is, the better it will work. Larger ones work better. As more of the beam is focused into a smaller narrow beam, the intensity(hot spot) becomes brighter, and will throw to a further distance.

That's why the "TurboHeads" work for the distance better than the regular heads. If you use double the power of the bulb, AND put on a Turbohead, then you are really getting something, because you have double the power, AND you are using more of it.

I don't sell flashlights, but I use them, and enjoy flashights as tools, and as a hobbyist.

Edited because I errantly used meters instead of feet in my original post.