It does depend on the speed you’re running.
If you’re running sub 7:30/mile, forget about anything <100 lumens, which includes nearly all the AAA strap headlamps out there from Tikka, PrincetonTec, etc.
Folks on BT rave about these, but they’re often running like 11 min/mile. Heck, even at 9min/mile, it’s hard enough to see where you’re going with these. You can do it, but it’s not enjoyable in the slightest.
A relatively inexpensive but excellent solution that’s been tried and tested is the Fenix L2D 2 X AA flashlight with a Jakstrap or other downward pointing headstrap. 180 lumens legit, for about 80 minutes. Piece of cake to change the batteries, so carry 2 extra ones if you’re going longer. The only catch is that you really should use rechargeables with this bad boy because it’ll burn through the set of batteries within that time - that’s actually a GOOD thing, though. Faster runners should avoid any light that uses small AA or smaller batteries and claims to have like ‘40+ hours’ of battery life. You don’t get anything for free - that battery life means much, much lower light levels. (You can turn the Fenix down or completely off with an easy click - do it all the time when going through lit areas or passing other folks head on.)
You can run 5 minute miles with this thing and still be completely fine. It actually makes night running fairly enjoyable (for me), since you can actually see where the heck you’re going even when going fast.