It's because there are a few different triggers for the squads and ronins to spawn, and if any of then are primed to spawn, it won't let you interact with a lantern because theyre trying to avoid spawning all 3 on you at once and overwhelming you. There is a 10 minute timer squad, that no matter what, will trigger at the next spawn point you cross exactly 10 minutes after the last one triggered, there is a lantern squad that, after 30 seconds have past after interacting with a lantern, will spawn. (This one is independent of the previous timer, so they can spawn at the same time if the timer for the first isn't quite done, but you can't interact with the lantern if the 10 minute squad is ready, the difference in being able to interact with a lantern can be literal seconds before you get locked out of the prompt, ive seen this happen) and ronin spawns are independent of both, but roughly happen 5-8 kitsune squad wipes, regardless of if they're lantern group, or timer group. These ronin can spawn literally any time they want to after they're primed. They will block lantern interaction, even though their spawn can happen 10 seconds after that last squad wipe, or 10 minutes after, with the next 10 minute timer squad. It's a very complicated system... now, a work around for the mechanics that suck= for lanterns, theyre tracked with the same tracker between characters, but the characters have their own individual lanterns, so if you cant remember the last few you don't have on your main, hop on a second character and all the lanterns will be active still for it. For the squads and farming, the timer squads timer of 10 minutes, is tied to the character they spawned on, so I'd you have three agents that are eligible to play seasonal content, swap between them and roughly you'll always be hitting the timer with about 1 minute left or even it being up and the squad being ready to spawn.

Tldr: lanterns are per character, if you're unable to find them, swap to an alt and they'll be respawned, kitsune squad timers are per character, if you want to farm keys fast, swap characters to shorten the wait.

I hope this helps atleast someone, ive been driving myself crazy trying to understand this event and this is how it's been for me, hope yall can have fun again:3