Luck is variance outside of the expected value given to limited sampling size.
You flip a coin 100 times, you probably won't get exactly 50 heads. You'll probably get something close but not quite.
If you keep flipping the coin 100 times, and keep recording how many heads you get, you'll end up with a normal distribution centred around 50. 50 will be the most common outcome, but not remotely the only outcome.
Now, let's say the NHL had perfect parity... Would every team end up with a 0.500 record? No. Just like the coin tosses, you'd have some teams with winning records and some teams with losing records.
We already expect, before accounting for some teams being better than others, for their to be a certain degree of spread in the standings due to luck.
Now, using this distribution and the real distribution, you can estimate how much luck is in the standings:
Gabriel Desjardins used this method comes out to about 38%, or 62% non-luck. This also gives us a theoretical limit to how well the best analyst or the best statistical model -or best combination- would be able to predict team and player performance.
Josh Weissbock as part of his thesis re-looked at this and found 38% as well (well, 0.376419753) and then used ML techniques to look at what is the predicted upper limit to predicting win% to see if it matched... and found: 62% upper limit. (Fun aside: he found the CHL leagues all being just over 70%, suggesting there is less luck at those levels, which makes sense as there is less parity).
Tore Purdy looking at team-to-team variation in point totals rather than record obtained similar results. (Fun aside: he looked at pre-2007 lockout seasons and found less luck (25-30%), which makes sense again as less parity).
I can break down how I determined all the other factors as well, but in each case it's something like this where multiple people used different methods and different tools to find similar results.