Luminosity value to use for the calculation of the habitable zone?
The number you need is the bolometric luminosity. This tells you how many Watts per square metre are incident upon the planet. That is true for the Sun and it is true for GL 570.

Beyond that, you will need to make assumptions about an atmosphere and an albedo if you are trying to calculate a realistic habitable zone. If you just assume the planet is like the Earth then using the same albedo value will probably do. But, because Gl 570 has a spectrum that peaks at 50% longer wavelengths than the Sun, then the albedo values at longer wavelengths are more important for a planet orbiting Gl 570. Whether that is bigger or smaller than the Earth would depend on exactly what sort of atmosphere/clouds/terrain were on the planet.