nit: seems like OP's definition of luck is roughly your definition of fortune. s/fortune/luck/rg in your post and I think you say the same thing.
Creating a new bucket to qualify things that happen regardless of skill seems redundant with the definition of lot. "Lot" in the context of OP's post happens despite skill.
I think there's a difference between lot and luck though. Lot is what you have before, luck is what you get during.
To crib from Warren Buffet [1], imagine a coin flipping contest. Everyone bets $1 and calls the flip of a coin. Miss and you're out. Betting pool is distributed among everyone else.
20 rounds in, there are 215 people with a few hundred thousand dollars made from a $1 investment and some time.
It's pure luck. They weren't even the one flipping the coin so couldn't have influenced the 50:50 chance even if they tried. That's luck.
Fortune is when you both bet and flip the coin and find a technique to influence the flip to be 40:60 in your favor and it works out.
Lot is when your dad gives you $100k to start a business.
Creating a new bucket to qualify things that happen regardless of skill seems redundant with the definition of lot. "Lot" in the context of OP's post happens despite skill.