Currently there are 2 different Labs in the game.
AVARICE.01 and Stress Test.
AVARICE.01 was added in version 1.30 and was the first lab created. It is mostly used for farming cosmic scripts.
AVARICE.01 has 7 different waves with each more difficult than the last, but also gives greater rewards.
At the end of each wave you have the chose between that waves reward or to carry on to the higher waves.
Each wave will give there own rarity script as a reward but you can only take one. It is recommended to go all the way to wave 7 as it gives a random cosmic script for it reward.
AVARICE.01 is limited to 1 reward pre 24 hours unless you have the VIP ticket, in witch case the reward cooldown is lowered to 2 hours.
You are able to do AVARICE.01 when it is on cooldown but you will not receive the level rewards.
With each wave you complete in AVARICE.01 the villains you have to beat will be of a higher level. At wave 1 they may not be much higher level then you but at wave 7 they will be a significantly higher level. This can make wave 7 a little challenging but if you are actively healing your scripts it is still rather easy.
Stress Test was the second lab to be added in update 1.36. It was mostly used for afk xp farming, but after update 1.38 it has become extremely hard to afk in and is now largely unused.
Stress Test is a experiment that is meant to push your party to it's limits, with villains levels increasing up to near infinity. Don't worry tho as there levels increase gradually by 5 levels at a time after each encounter.
Stress Test starts at a level very close to your lowlifes with makes it easy at first, but after some time the villains will be 100 levels over yours or even more.
When you eventually die in Stress Test the level you died at will become your new high score and is automatically submitted to the leader board. Every time after that you will go up 10 levels after each encounter until you hit your high score, at that point it you will progress at the usual 5 levels per encounter.
There is no real rewards for Stress Test apart from decent amounts of xp for killing the higher level villains. That's why before update 1.38 most people would typically afk overnight in Stress Test, because there are no rewards to collect your scripts would infinitely kill villains before they died. You cant really do this anymore because update 1.38 removed a lot of survivability scripts have to they die a lot quicker now, this has left Stress Test relatively useless for now.