This was always going to be the danger. "LA won it all when they were the 8th seed so why can't we".
Long answer:
Since the NHL expanded from 6 to 12 teams in 67-68, only one 8th seed has managed to win the cup. One 8th seed in 46 years. Wait, it gets better.
Stanley Cup wins by seed:
1st seed - 24
2nd seed - 11
3rd seed - 6
4th seed - 2
5th seed - 2
6th seed - 0
7th seed - 0
8th seed - 1
In 45 seasons (no cup in the lockout year) only once has a 6th, 7th, or 8th seed won the Stanley cup. Awesome odds. Just making the playoffs isn't good enough. Unless you make the playoffs with home ice advantage, you're chances of winning are ridiculously low.
Then you look at the LA team that did manage to pull it off and ask "what makes them different". A perfect storm. They went from Terry Murray as a coach (13-12-4) to Darryl Sutter (25-13-11) and were obviously, as the records show a completely different team after that change. They also got significant added help at the deadline by acquiring Jeff Carter who had a significant impact on their success (funny sidenote, most people here didn't want to touch him with a 12 foot pole because he wasn't a healthy addition to a cup contending roster... apparently).
But why is this so? It is so because 98% of the time the best teams in the post season are also the better teams in the regular season. That's not an exaggeration.
Short answer:
Because that almost never happens, that's why.