@JVL, I don’t think the result is meant to be like the photo. If you want to etch a photo, you may as well convert the original to greyscale and print it.
The results from this site are more like a pen and ink rendering, so there will be sharp lines and it’s possible that some detail may go missing. As a suggestion, try using a colour photo and a greyscale copy. You could get entirely different results.
You could also play with the brightness, contrast and/or sharpness of your original using a free program like Irfanview. Every change you make will produce a different result.
This is what I get using just Lightburn.
It’s still not as good as Nicky’s but its getting better.
As you can see I’m still struggling with the vertical lines.
I’ve only ever done one etching so I don’t know a great deal about the patterns. In the printing game we called them moire patterns and we resolved the issue by scanning at a 15 or 45 degree angle. I’ve read about your problem several times and there seem to be settings in Lightburn that will fix this. Sorry but I can’t remember where I saw it. Maybe in a Youtube video.