There's certainly some good suggestions in the thread so far. Now, one of the reasons I run 1e is because the characters are a bit sturdier than they are in B/X, OD&D, etc.
Here's the thing. Here's where I disagree with OSR orthodoxy. The idea of "combat as a fail state." The problem being, I've never in 35 years of running the game, had someone at my table who didn't like combat. Who didn't want combat! I'm sure they're out there. And yes, there are a lot of things that happen in D&D that are exciting and fun and don't require the combat tables.
But, combat is where it's at! Take every advantage you can, plan, play smart, use every advantage and strategy, be cautious and judicious, by all means, but at the end of the day who wants to play in a D&D game where you get to level five and have never killed an orc? Or, have never fought in a dangerous, fever pitch battle that you survive by the skin of your teeth and get to brag about for months or years to come? Unless you've created a super tame dungeon and some real quiet random tables, combat and combat death is going to happen and blaming the characters for being too lame to avoid it is unreasonable and undesirable. Few wanted to avoid it in the '80's and few want to avoid it now. I've never had a party play through G1 and just, you know, talk to the giants. I've never had them trick the giants into leaving, though admittedly, that would be pretty cool. G1 is a slaughterfest. And fun as all hell to run or play through.
My son is 15. He and his friends play 1e/Osric. They're also into super hard and retro video games. Like Spelunky. Ever play Spelunky? Fuck. Spelunky is hard, unforgiving and there's no save function. A lot of things can kill you with one hit and it takes skill and determination to get anywhere with that bloody game. Not every young person wants a game that hands everything to them. There are always going to be gamers who want the Hard Stuff!
Some decent death rules are desirable. Nothing as easy as, say 5e, but something more forgiving than death at 0. And make resurrection plausible by at least fifth level or so. Charge out the nose for it, use it to force quests, whatever. But once res is on the table, characters get a lot more relaxed with the idea of PC death. At that point, a TPK is what they worry about.
Old School play is probably never going to be for more than a relatively small sub section of RPG gamers. And that's okay. Get out there, talk to people, recruit people totally new to the game. Play via internet, if you've got no other choice. It isn't bad and still feels like playing D&D.
And do remember this. Three or four years from now, the players are unlikely to remember much about the time they casually dispatched the Lizard King's guards after putting them to sleep, then sneaked into his treasure room while Mr. Lizard was busy eating lunch, stole his treasure chest and coolly sauntered out of his dungeon.
What they're going to remember forever is the firefight, down to the wire, one or two PC's down, all out melee, which they won with grit, daring and a timely lightening bolt or critical hit, finally killing that bastard Lizard and looting his treasure, limping out of the dungeon and calculating how much they would have to spend on getting a fellow PC resurrected.