It seems that normal difficulty is a matter of luck. If you don't get the right things, you can't win.
I've found the exact opposite to be true. As far as I can tell, you CAN lose due to luck, but it is vanishingly, terribly unlikely, and the odds are weighted in your favour.
I haven't lost a game in 9 runs right now, and since I've only been doing runs for the crystal ship I've been doing stupid shit like skipping sectors and generally not trying, and even combined with piss poor luck in a few of those runs I've still had no trouble beating the game. And this is on normal.
I find that unlike many games of this sort, FTL comes down almost solely to skill in the end. It's called a crew management game for a reason, and good micro plus decent preparation are more than a counter for 99% of the terrible luck situations the game throws at you.
And since you can pause, it's not even about being able to do things quickly - it's just knowing what to do, and realizing that most bad luck is just you playing poorly.
My last loss was with the Federation Cruiser and this is because I broke my own rules and played /stupidly/, by focusing on the artillery beam instead of capitalizing on the opportunities the game threw my way - opportunities most people would have seen as bad luck, because it didn't help them get what they want.
Almost everything that IS truly luck-based is completely optional and lets you know up front (white options with a "don't get involved" situation), and once you learn the likely results you learn when it's worth going for (hint: Don't take bets you can't afford to lose)