I just managed to get 2 characters out of lab in a row and didn’t need heavy RNG favor for it.
Here’s a guide to reliably escaping out of a lab. No heavy luck required, only lack of heavy un-luck.
Guide assumes some basic player skills, such as grinding up fabrication to 2 using only wood and a knife, getting 0 torso encumbrance and not panicking at the sight of “famished” in status bar.
There are 2 reliable escape options: fire, bashing. If you choose bashing, you’ll need a lot of strength at char creation.
You need 18 to bash down walls with 2-by-sword or 11 to use a quarterstaff. You have (str+bash-29) in 180 chance to break a wall with each hit, where “bash” is BASE bash damage (reinforcing and chipping doesn’t count), so low strength will heavily slow down the process.
To acquire a quarterstaff, you need 2 fabrication and 2 bashing weapons. If you grind up tailoring and armor up, you can find a manhack and keep missing it with a bashing weapon to grind the weapon skill. Grinding fabrication is trivial - just craft wooden stuff. You could try to get craft homewrecker (28 bash), but getting that 8 long strings would require disassembling 24 rags (an entire day worth of work) while food is scarce. If you’re really lucky, a zombie might spawn a sledge hammer.
Once you get the tool, just wait for the night, go up and bash the wall down. It’s 2 tiles thick.
Fire method is easier - just start a fire where the turret won’t see you and wait on the stairs until it burns down walls. It is also more risky and luck-dependent, but can be attempted much earlier.
You’ll choke on a lot of smoke and will have to go down stairs a few times to cool down and you will have to push through smoke and rubble before smoke disperses or the turret will shoot you. Better haul a lot of bandages, because that smoke will damage your torso for long after you escape. You’ll also have to manipulate reality bubble to acquire a rain to speed up flames going out. Flames won’t kill the turret, so make sure it won’t see you.
Also, burning building is loud. If there are animals/zombies nearby, they’ll probably come to watch. Better hope they’re dumb enough to get into the fire or weak enough not to be dangerous (my first escapee immediately got attacked by 2 wolves at 20% torso hp and survived only due to good stats).
Teleport, armory full of explosives, CBMs etc. are more luck than skill and so they aren’t a part of the guide.
You can tell a room has a turret because it will have lit up walls. Big rooms can have turrets far from doors, but those won’t see you if you don’t have a light source and stand in the darkness while opening the door. Peek around corners (default ‘X’) if there are no walls/doors.
You can tell room has mobile creatures in it by knocking on (smashing) its wall and waiting for reaction - zombies will hear the knock and get angry and start whacking the wall, robots will start moving around. Metal doors can take all zombie hits (except maybe hulks, but those don’t spawn here), so if you see something scary, just close the door.
If you’re going the bash route, you’ll have enough strength to take all but the strongest zombies (bio-ops, brutes) without a lot of damage. You still want to avoid unneeded battles with zombies because while bandages and cotton balls are plentiful, disinfectant and first aid kits aren’t. Cauterization is very unreliable, so infection may often be a death sentence.
Skitterbots are dangerous if you have low dex, low melee skill and bad weapons. They have quite a bit of armor, so light weapons aren’t all that good against them. They have no light source (unlike manhacks or turrets), so telling them apart from zombies requires being close.
Manhacks are hard to hit, but very weak. They also have hit and run flag, so they’ll disengage after every hit. Just hide in the darkness if you don’t want to fight them. You can train bashing and melee by missing them with a plank.
Broken cyborgs are great punching bags. Don’t pulp or butcher their corpses before you get bashing to lvl 2 if going bashing route. You can miss them with heavy weapons (10 bashing or more) or hit them with light ones (a 0 dmg item will train bashing, but won’t deal damage unless you’re hulk mode strong). If you’ve got 0 torso encumbrance and didn’t gimp yourself by lowering DEX, you will dodge most of their hits and even those that hit are very weak.
Robots can’t smell you, but some of them can hear stuff. If you see/hear a dangerous bot creeping around, stand still and throw something to lure the bot away.
You have to go fast before it all runs out.
Humans are nutritious, but morale penalty from eating them will stack and prevent crafting. If you get famished, cut up one of those naked corpses, cook it all up (make sure you cook enough before starting eating) and eat until full. It’s a good idea to eat before sleep - even if you get -400 morale, most of it will go away before you wake up.
Water isn’t exactly rare and there are rooms with infinite water, so thirst is only a problem if RNG hates you or you go slow and don’t map out enough of the lab before starting grinding skills.
When cooking food, keep the flame tiny and stand far from it. You’ll still choke on smoke, just much less.
Lab characters can be even better than Really Bad Day ones, because they can pick mutant traits. The only mandatory trait is Night Vision, but it’s an amazing trait on everyone.
You don’t need INT to escape. Go full hulk. PER is useful if you haven’t memorized where dissectors spawn and for goo pits. DEX is amazing for early combat.
You can lie down on blankets to warm up. If you do it on solid rock while not tired, you’re unlikely to fall asleep.
Minor Radioactivity won’t trigger Radiogenic. In fact, it won’t do anything to you. Free 4 points, but make sure it doesn’t mutate further - non-minor Radioactivity is PURIFY IT RIGHT FUCKING NOW kind of mutation, unless you want to wear a cleansuit/hazmat/full power armor every time you want to take a nap or craft something. Radiogenic and iodine won’t help much here.
In the end if RNG decides that you’re supposed to die and places upstairs in sight of a turret, sends bio-ops at you, spawns you near alien containment (flaming eye can free all the other stuff) or does other similar bullshit, there’s not much you can do. But those are rare cases and a great deal of lab survivors can actually escape and mutate into free people. Free people with better stats than most other free people.