First off, let's all remind what PDO is:
In other words, PDO is the sum of shooting percentage (the number of goals scored divided by the number of shots for) and save percentage (the number of shots saved divided by the number of shots against). Usually, PDO is evaluated at 5-on-5, but for the discussion below it's irrelevant. PDO is a team statistics, but apparently ("a player" in the quote above) it can be evaluated for players too, I suppose similarly to +/−.
Myth No 1
PDO converges to 100
[A side note: actually, I've seen references to the law of large numbers and even to the central limit theorem. From that it is claimed that this myth follows from mathematics. A half-educated nerd is worse than one hundred fools.]
Imagine a league made of Team Canada and Team Kuwait (no disrespect, I just took the first team and the last team from the IIHF rankings) playing 82 games. Each game finishes 10:1, with shots 50:10. Team Canada PDO is 10/50 + 9/10 = 110. Team Kuwait PDO is 1/10 + 40/50 = 90.
This is of course very generous, most probably it will be like 20:0 and 80:5, but you get the point: it is league-average PDO that "converges" to 100, not individual team PDO (league-average PDO does not even "converge" in layperson's terms – it's always equal to 100 by definition).
In a real, competitive league like NHL, individual PDO converges to something between 98 and 102: in the last 6 seasons, only 14 teams out of 182 finished outside this range, roughly 8%.
This very narrow range in PDO (root-mean-square deviation of 1.13 points over the last 6 seasons) gives the impression that any difference in PDO is simply due to statistical noise – i. e. "luck".
Myth No 2
PDO is a measure of "luck"
From the discussion above one can see that PDO in NHL varies within about 4 points. Keep in mind that this difference is due to shooting and save percentages.
4-point difference in SV is the difference between Vezina-level goaltending and a bad backup. Imagine an average team with Tuukka Rask in goal. Replace Rask with whoever is current Toronto backup. It's clear that PDO will go down because Rask is better than the Toronto backup, otherwise there is no point to pay them vastly different salaries.
It is quality, not luck (apart from being "unlucky" to have a Toronto backup instead of Rask in first place). Good teams (like good goalies) have higher PDO (SV) and bad teams (like bad goalies) have lower PDO (SV).
The same applies to shooting percentages.
Myth No 3
Teams with high PDO crush next season
This myth highlights a very interesting fallacy, the one that statisticians call "confirmation bias": we look at high PDO teams that crush, but we disregard high PDO teams that DON'T crush.
Let's look at the data for the last 6 seasons (excluding 2018-19 for obvious reasons):
Top-5 PDO teams: 9 didn't make the playoffs next season, 16 made.
Top-5 CF% teams: 8 didn't make the playoffs next season, 17 made.
On top of that, 7 out of 30 Top-5 CF% teams didn't even make the playoffs in the season they posted Top-5 CF% numbers (compare this with just 3 teams PDO-wise). Clearly, PDO is not much worse than the cherished Corsi in predicting postseason success.
[A side note: based on intuitively clear definition of "postseason success", I calculated correlation coefficients for how far a team went in the postseason versus its regular season PDO and CF%. PDO appears to be a BETTER predictor than CF% (correlation coefficients of 0.414 and 0.339 respectively over the last 6 years) – but this result is for another discussion.]
Is there any luck in PDO? Yes, in short term, there is some luck there too (as almost in any other number), but usually one is not required to parse through PDO to see that. For example, right now the Islanders are in a 15-1-2 point streak, and the Stars are in a 14-1-1 of their own, their PDO over that span must be huge (102.7 and 103.7 respectively, via nhl.com), but I don't need PDO to understand that close to 150-point pace is unsustainable for ANY team.
So, let's give a rest to PDO as a measure of luck, leave it to uneducated folks like Lambert and Luszczyszyn.