Cree Component XLamp XM-L LEDs
Rated at 1040 lumens at 10 watts. So theoretically, 4 of them can produce 4160 lumens if you're able to deliver the required current and do everything else right. I suppose you can overdrive them too to get even more, but let's go with those numbers for now.
26650 batteries max out at 3.7 V but on average run at around 3.2 V. At 3.2 V, you'd need 3.1 A per LED, which means that in this configuration, each battery needs to sustain 6.2 A. All this assuming "best case" according to manufacturer ratings.
Now it will depend on whether or not your batteries are up to the job. From googling around, it looks like many 26650 batteries have their maximum sustained discharge current rated at or beyond 10 A, while others (due to the PCB?) only give you something like 4 A, so YMMV.
So, theoretically plausible given the right batteries. How the light actually performs is a different question. The "15 watts" makes me somewhat suspicious, because even if that's 15 W per battery, that still leaves you short by a couple of A.