So there's two different kinds of deaths going on here:
1) Players make risky or bad choices, which results in a bad thing happening to the PCs. In CC, I think the twins only come if they steal the tiara, right? This happened to my party - the group decided to leave it alone, except one player decided to sneak back and snatch it, which unleashed the twins on them. They were luckily able to defeat them. The party thought this was a random attack, only the thief who took the tiara knew it was likely happening b/c of his choice.
2) Bad luck (ie, you get the most deadly result on a random encounter roll, or some such thing). I was playtesting the new LotFP rules and made a survival roll for the party, which resulted in one of the PCs tripping on a rock and taking d8 damage. It was enough to kill them. They were not happy about this, especially since they made the choice to leave the dangerous dungeon and get back to safety.
Number 1 I'm not concerned with. If players don't seem to be getting it, you may want to reveal some of the behind the scenes stuff after they've finished with the consequences. Let them know that they would not have fought the twins if they hadn't stolen the tiara.
Number 2 does kind of suck. I think having random bad stuff happen is okay, but random death isn't.
At any rate, I've mitigated both of the above with a few things.
1) Instead of dying at 0 hp, instead the PC loses a permanent point from their CON, and a permanent point from a random other stat.
2) They have a Luck stat. This is an average of all their stats at character creation. From then on, they can burn a point from this stat to reroll any die. However, this is also their stat for initiative, running away, and figuring who the "bad thing" is going to happen to (ie, I ask all to make a roll and the one who rolls worst is the one that gets the random attack). I also use this for when they try something possible but risky, they just roll their luck and don't roll a 1 to succeed (this last one requires you to have unusual dice, like those from Dungeon Crawl Classics).
3) At character creation, they create four 0 level characters and choose one to put at level 1. They can bring the others along as helpers who can take on some of the risk, including, when running away, these are always the slowest characters. One or more might die, but it allows the leveled party to escape.
Doing just one of the above might be enough to give your players the boost they need to survive. I decided to implement the above b/c I found that the unavoidable instant deaths in LotFP were a lot more enjoyable to experience then the dying through hit point loss method, and my players started to be too afraid to interact with anything, so I needed to give them a bit more confidence to explore more.