How To Improve Item Level

[Kuroka]

You're a level 54 Lancer. Go do your class quests to pick up your Dragoon job stone, for one thing. By level 50 you should have already gotten your ilvl 90 gear for the entire left side. With that, you probably wouldn't even need to be worrying about your accessories.

But your accessories are also wildly outdated. If you've gotten absolutely no replacements from any of the dungeons leading up to that point, and have not gotten any that may have been available from quests (sometimes side quests), you've almost certainly been checking the wrong shops. Your Grand Company very likely has a few pieces that would be better. Pretty sure the shops in the main cities all have wide ranges of items. There's even the entire Marketboard you could be searching.

I get that you're here asking for help, but, this is, like, tutorial-level knowledge, leaving me to assume you're likely skipping over literally everything the game has been trying to teach you.

This. Im the very first to explain but this is like, "why are my hands burned after touching fire?" xD

As others said before, do you jobquests, grab some sidequests that reward gear - you can see in the preview. Also you should have gotten some at the dungeons you needed - if not do some runs of your highest dungeon for gear.
And you can look for gear at your Grand company, but i guess you rank gonna be too low...?

Also as youre 50+, you can get ironworks gear at mor dhona, from Auriana at x22:y6,7.... though i guess you wont have poetics yet?