Ok, yes, I see that it doesn't work on my end as well. However, I figured it out. You need to go to your base NL directory, go to gfx => menu, and put your custom levelinfo_icons.png in there. Be sure to back up this folder first, as it will ask if you want to overwrite the file. I have confirmed that the new icons work when this is done. I've also confirmed that if you take it out of your level pack folder, the custom icons still load, as long as the .png file is in the gfx => menu folder. Therefore, apparently it doesn't work if it's in your level pack folder, which I think is really strange, as all other graphic files work, so surely having it in there should take precedence over everything else, like how having a music.nxmi file in your level pack folder takes precedence, and only then if NL can't find a matching title track, then it falls back to the standard music rotation music.nxmi file in the data folder located in the base NL directory.
Let me know if this works for you!