LightBurn will automatically resample any image to match the output size and DPI specified. You’ll get the best results if you start with a high quality photo, but it’s not necessary to exactly match the source and output DPI.
The most important part of producing a photo with a laser is the beam width when focused - If your beam produces a point that is 0.1mm (~250 DPI) then trying to output an image to the laser set to 500 DPI will cause a 50% overlap between neighboring lines, and that can end up burning out all the detail you might otherwise have. This is slightly more true when using dithering than when using grayscale engraving, because of the way they work, but in general, you want to output at a DPI that matches your laser dot size, or is close.
Next is the material. Wood will char around the beam, whereas slate or anodized aluminum has very little “spread”, so you’ll get a narrower point on those than you will on wood. Run some small swatch tests with different DPI settings, look at the results through a magnifier, and pick what works for your laser and material. Try to find the setting at which you can no longer see individual lines in the engraving.
I looked up the Opt Lasers model you mention, and their specs say the spot is 0.1mm at a 30mm focus distance, so I would try between 0.1mm and 0.08mm (250 to 320 DPI). The beam tends to have higher intensity in the middle, so you can go a little smaller than the dot size without affecting quality.
None of this will help much if the source image is poor, so good resolution and contrast are important. LightBurn can increase contrast, and even edge detail through the use of some of the built-in controls, but a good quality photo with good contrast often works very well without adjustment.