It sounds like your core question here is how to convert the "1536 LM" — presumably meaning lm, the standard prefix for lumens — to an exposure value which you can use to find camera settings. That's fundamentally the same question as How do I compare a continuous light panel's brightness vs. flash through a softbox? There I was starting with candelas per square meter (cd/m²), but as the first answer there shows, they're (basically) convertible.
However, answering your question is hard, because lumens are measured over the angular spread at which the light is emitted (see How to relate LED Lumens to Lux at a given distance? for some very mathy details), and we don't know what that is from your product listing, nor how well that corresponds to your need.
That said, the 1500 lm value¹ is roughly the amount of light one would get from a 100 watt light bulb. If we assume that that's accurate for the amount of light falling on your subject, we can estimate that you'll have an exposure value of about EV 7 at about a meter away.²
Now, you've given f/2.8 as your widest aperture, and ¹⁄₁₀₀₀th as your required shutter speed. That works out³ to EV 13 at ISO 100. Since 13 minus 7 is 6, we need to make up six stops. We can do that by raising the ISO, of course — and going up six stops from ISO 100 gives us ISO 6400.
So, you can probably make this "1536 LM" light work by using ISO 6400. However, throwing in a dash of healthy skepticism over the nominal ratings of generic-brand lighting products might bring you up to the camera's maximum ISO of 12800. And, amplifying the available light that much may not produce images you're satisfied with. Bottom line, I'd suggest more light than that panel alone — and probably a lot more.
- "1536" is weirdly over-precise, and I'm certain comes simply from multiplying the number specified for each LED by the 256 LEDs in the panel — working back, that gives LEDs of 6 lm each. Of course, it's very, very unlikely to be really exactly six, so 1536 instead of 1500 is very silly.
- From this site, where a pad of paper located 4 feet from a 100 watt bulb is given as EV 7. Or multiple similar sources.
- Easiest way is simply to look on Wikipedia's EV chart.