Crank-arm fell off *after lube* Background
I've had my bike for several years and it's been fine with moderate use, but this summer, I ended up using it a lot (I rode almost 200km in less than three weeks).
Problem
It started squeaking pretty badly, so I sprayed some lubricant around all of the joints (pedal, crank-arm, etc.) then took it out for a spin. On that very first ride after the lube, the left crank-arm nearly fell off; I though the pedal broke, but when I stopped and checked, the nut had come loose. I managed to use my keys to tighten the nut and repeat every block or two until I got home.
Attempted fix
At home, I used a 14mm socket wrench to tighten the nut, but it keeps coming loose. I've resorted to carrying the socket-wrench with me when I ride and stopping to tighten it about ever kilometer. 
Research
I've read some stuff about the holes in the crank-arm wearing out and worn nuts and how Loctite isn't a solution and such, but none of them mentioned lubrication. My issue started immediately after I lubricated the area around the nut, so logic would dictate that it allowed the nut to slip. I've included a photo (fig.1) of the crank-arm hole and nut. To my eye, the hole doesn't look worn (I assume the bulging around the edges is intentional), but the catch-teeth on the nut do seem worn/flat. 
Question
Anyway, I'm wondering if lubrication is indeed the problem and if cleaning the lubrication off (and maybe applying a mild adhesive like Loctite or just hairspray) would suffice.
Appendicies
Figure 1: Crank-arm hole and nut
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.