The source image (your PNG) can be higher than you need, and that’s fine - it’s actually good to have about a 500 DPI source image or better, if you can, as it gives LightBurn more information to work with, and can help.
The output DPI is the more important one - that controls the dot spacing of what LightBurn sends to the laser. In LightBurn, DPI and Interval are just two ways to control the same property - IE, the spacing of the dots / lines that it sends to the laser. If you use too high a DPI value (or too low an interval) the lines end up overlapping, and it turns the shading into mush. This is really important for things like photographs with smooth shading, but much less of an issue for simpler stuff like the logo you posted.
This might give you a better idea of what Interval / DPI do: Image engraving guidelines