The Laboratory facility simply serves the purpose of increasing the efficiency of research in your base, shortening the process by a fair amount. It's not required to be able to conduct research in general, but it decreases the time needed to perform those actions - 2 scientists will decrease it by 22%, allowing you to save a few days on some of the longer projects.
As it's not the most important facility in the game, you don't have to rush it and you should first focus on constructing enough Resistance Comms, as well as the Proving Ground, Guerilla Tactics School and / or Psi Lab facilities.
Upgrades and staff influence
Construction takes 16 days.
Monthly upkeep cost - 35x Supplies.
- Allows you to fill the facility with up to two scientists, significantly decreasing the time needed to complete a research.
Additional Research Station: allows you to fill the facility with a second scientist.
Cost: 125x Supplies, 5 Power. Monthly upkeep cost - 40x Supplies.
Staff: up to two scientists can be placed here, both decreasing the time needed to complete a research by 11%.