The hole on the left picture should be perfectly square. It's so badly worn that the crank and possibly the bottom bracket as well should be replaced. It is not safe any longer.

This job requires special tools that are too expensive for a one-off job. Because of that it is a job for a professional mechanic at a bike shop. There are also many different standards of bottom bracket that each asks for its special set of tools.

Your crank arm is toast.

In my experience, if a square taper ever gets loose while riding, even once, it's done. Retightening the bolts buys you a few miles at best but it'll loosen up again before long.

I think the connection to lubrication is coincidental. You said the problem started after you applied lube, but that's not true. You did that because it was squeaking badly, meaning the problem was already underway. When it began to squeak, its demise was already imminent. Spraying lube did nothing to speed up or slow down the process. Additionally, the taper should be lubricated lightly when installing.

The problem was an insufficiently tight crank bolt, possibly from the day it was bought. When you replace the crank, make sure that bolt is tight. While others disagree, I find it cannot be overtighted as long as you use a normal sized driver, and that you don't have gorilla strength. Give it some muscle so it stays put.

Additionally, stop riding with that crank immediately, or you also risk wrecking your bottom bracket spindle too. BB spindles are made from hard steel, so they're not one-and-done like the crank arms are, but they can be worn down too if careless. If that happens, no cranks will fit snugly, and you'll wreck another crank arm, or more.