It appears DynamicLight is not accepting any of AdditionalLanterns items as part of the selflight config.

Example dynamiclights_selflight.cfg that should in theory work:

{
  "itemsList": [
    "{lightLevel:14s,nameId:\"minecraft:torch\"}",
    "{lightLevel:15s,nameId:\"minecraft:glowstone\"}",
    "{lightlevel:15s,nameId:\"additionallanterns:basalt_lantern\"}"
  ],
  "notWaterProofList": [
    "{nameId:\"minecraft:torch\"}"
  ]
}

I also attempted with the anyNBT variable, but same result. I will note that with the default minecraft lantern (minecraft:lantern) it works.

After checking wiht AdditionalLanterns' developer, who has configured the mod succesfully with other dynamic light mods, it appears that the issue should be on this side - the nameId appears to be correct, and was taken using CraftTweaker's commands.

Well this was a fluke on my part. As you can see, lightlevel is misspelled (no capitalized l). Correctly fixing this makes the items work properly.