In the winter, sunset can be 3-4 pm here, so most runs are night. Therefore, getting by with a low output solution doesn't make sense. I also don't want a different light for skiing vs. running vs. cycling, though I mostly ski and run in the winter. Bike and skiing headlamps, as well as orienteering headlamps (same as cross country skiing lights) are very well developed and useful, unlike the headlamps marketed to American runners. There are also low cost bike lights that aren't anemic, so that's what I'm using now.
I started doing night trail runs in the '90s in CA. If running in neighborhoods, multiuse paths, roads, no light was needed to see, but trails were another thing. There was a 12 mile loop that I often ran that was about 7-8 miles on trails. Most of the time, I would just go without a light. This would sometimes be totally fine when the ambient light was sufficient. For example overcast conditions would create a kind of glow even under the oak trees from light refracted from moonlight, distant city streetlights, and stars. Other times, such as with strong direct moonlight, or just very dark wet conditions, I wouldn't be able to see the ground at all under the trees, and it would feel like a black hole under the trees. I'd have to slow down from my daytime pace, but I enjoyed doing it for the adventure aspect. Animals active at night, like deer, mountain lions, bobcats, coyote, fox, squirrels, wild turkey, wild boar made it even more of an adventure. The headlamps that I sometimes used in the '90s were close to useless, except to help me see the ground under the trees, still at an inching-along pace. These headlamps included the Princeton Tec Solo, a 2AA halogen with very low lumens, and then a Princeton Tec Aurora, a 3 Nichia? LED headlamp with maybe 10-20 lumens.
When I joined this forum, I think my first post here was a review of the Princeton Tec EOS, which had just come out and would later be a favorite for modifications. I think it was around 30 lumens stock initially. That made it much more useful that the Aurora, but the beam was too narrow, and it was still too dim. I eventually modified it with a Seoul P4 emitter upgrade, and a Mc-18(?something like that?) reflector swap that made it the first headlamp that I had that was actually functional for running at night on trails. I think it put out about 100 lumens after the modification, and the beam was finally wide enough that I could point the hotspot up the trail while still being able to use the spill to see in front of my feet, as well as the side peripheries. I also added a homebrew external pack, so I could use it on the high setting continuously because the lower levels were useless for running. So I'd say that about 100 lumens is the minimum that I'd find useful for running, and that's only with a good optic or reflector that provides a good mix of spill and distance at the same time. Running pace would be reduced from daylight running pace. Maybe 7-11 minutes per mile on trails in dry conditions or packed snow (in AK by then).
Rain and wet ground makes things really, really dark. 100 lumens gets mostly absorbed, little gets reflected back, and it might only be bright enough for walking pace some nights on rooty trails. Sometimes even 1200 lumens in those light-sucking situations is just enough for running. You might have experienced similar situations while driving two lane road in middle of nowhere in the rain with faded lines, where you can barely see the road. When snow arrives, everything is much improved at night, and is much welcomed after a dark fall. Not all snow is equal though. Sometimes it's no more reflective than dry ground, but it's better than wet ground.
I have since used a succession of bike lights for running since the first Magicshine MJ-808 ("900 lumens", really about 600 lumens initially) maybe about 10 years ago, which was a copy of the Lupine Tesla. This was followed by the Gemini Lights Xera (about 800 lumens? initially, single emitter), Gemini Duo 1500 (dual emitter, 1200+ Lumens actual), and now a cheap copy of the Duo, the Yinding 900 (actual 1200 lumens). I have mostly used 2x18650 packs with my bike headlamps, with a burn time on high about 1-1.5 hours. Since most of my runs or skis are about 1.5-2.5 hours, I tend to use the medium setting most of the time to make sure I don't run out of battery life before I'm done.
On the Yinding, medium is about 600 lumens. Pace varies a lot depending on the trail and what I'm doing, but I'd only drop to low (maybe 300 lumens) if I'm walking or running up a ridge/mountain at night, or anticipate a long outing and don't want to run out of battery life. One purpose of having sufficient light is to not have a difference between my nighttime pace compared to my daytime pace. I have a lot of Strava course records for downhills that I actually have run at night. Paces for some of those nighttime efforts include about 4:47 pace per mile average for 2+ miles down a trail with 1200 lumens blazing. I sometimes top out close to 4:00 pace (15 mph) on parts of those downhills.
Mountain bikers typically run one light on the handlebars and one light on the helmet, each with 800-1500 lumens max or more. A strong runner on trails is really not much different than a mountain biker. I think I read that typical local cross country mountain bike races, semi-technical and with ups and downs are won at 9-11 mph (daytime). I also run 10+ mph in the local trail races that are held on the same trails. When a mountain biker is riding uphill as slowly as a typical runner, they might turn down their lights, but they don't turn their lights down to 100 lumens for good reason. Their lights vary, but have a good broad spread for at least one of their lights to make sure it's not tunnel vision. My Yinding has a very broad spread of light with a good center weighting (
https://youtu.be/RKj0zs9IbdY ). 300 or 600 lumens, when spread out, isn't overpowering. And when compared to 100 lumens, you just see better. You see the roots, ruts, rocks on the ground. You don't have tunnel vision. And, importantly here, you see the eyeshine of the moose and bears in the woods (or neighborhood here) before you run into them, even if you aren't going fast.
Other conditions: In a blizzard with really blowing snow, I've found that the more lumens the better. I've been in a blizzard where 1200 lumens was just enough (and wanted more), while 600 and 300 were too low.
In Europe, especially Scandinavia, where it's as dark as it is here in the winter, and where orienteering is popular, they have the right idea with their orienteering/skiing headlamps. There, runners racing through the woods at night use headlamps like the LEDX Cobra with 6500 lumens - no one there thinking 100 lumens is enough for running in the woods. Here's my thread from last winter:
http://www.candlepowerforums.com/vb/showthread.php?429338-Headlamp-Porn-(Night-Orienteering)
