I like the idea of a rank 4 toolbox LS deck! Whenever we get the new Minerva I'm sure it'll be easily adaptable. Obviously I don't actually know how it works now, but here's a few things I'm thinking might be worth taking a second look at:

2 Wulf, 1 Felis: Generally speaking, I'd only run one of each, but I understand the appeal - they make Rank 4s much easier to make. But unfortunately, they make brick hands way way more common.

Only 1 Lumina, Raiden, and Lyla?: Lumina is one of the best Lightsworn cards you have. It lets you fill the field much easier, and while it sucks she's a level 3 and can only go into Rank 3s, it lets you make a synchro from having an empty field, and lets you dump Wulf or Felis from the hand. Raiden is free milling, a good attacker, another level 4, and a tuner. He is the Lightsworniest card we have. Lyla is your MST, plus milling, plus another level 4, she's great. You can use her effect and then overlay her so the position changing isn't annoying. All of these are at least worth 2 spots each, if not 3.

1 Judgment, 3 Diabolos: Diabolos is not a bad card by any means, but its effect is nowhere near as solid as JD. Honestly its best ability is to be able to banish Eclipses and get JD in your hand. I'd swap the ratios here.

Ghost Ship: An interesting tech card to get rid of Eclipses from the grave, but damn is it useless once it's on the field, as the only level 5 you have. I understand the appeal, but maybe something like {{Freed the Brave Wanderer}} would be better, so you get a decent effect for your banish at the same time. plus you can search Freed with ROTA. I guess you can summon Grepher by dumping it, but then... do you need Grepher anyway? It doesn't seem to be all that great.

Effect Veiler instead of Breakthrough Skill?: Don't get me wrong, a LS deck should primarily be a monster mash, BUT it should be monsters that you don't mind losing to the grave. Breakthrough Skill is helpful even when milled, Veiler is not.