This is what I believe:
After many years of the current League of Legends time, the technology of the world had increased drastically and reaches a point in which a human revival can be done, however it needs a host (a dead person) to do so. The revived would have their memories before death and would have the more strength than they had before dying, in term, weaker ones can become stronger, the strongest in all of History would be unstoppable. So, this process is only worth to be done on powerful humans back in time. This process was first done by the Ionians, which they tested on some normal dead people and was proved successful and was to move on to the next stage: PROJECT. PROJECT's goal is to create super-human soldiers with extreme strength and defense, the scientists first found Zed's grave and dug him out (he was very powerful back then), planing to test on him first.
Using the same procedure, Zed's body was revived to full health but is replaced with a robotic body that can do crazy stuff and withstand extreme conditions. To avoid a disloyalty, Zed's memories had also been replaced with a chip that holds the things scientists wants them to do, Zed is the only one who was able to do this (because he's evil like the scientists).
While Zed is the first successful PROJECT member, Fiora, Yi, Lucian, Yasuo, and Leona was also on the way of becoming a PROJECT member. However, they all overrode and rejected their memory reprogramming (because they were good people) and realizes that they had been revived and is now in the future. In the YouTube video PROJECT:OVERDRIVE, it first shows Yi's distorted memory and then "tortured by the scientist" and breaks out of the unguarded lab, this might be what one of the process looked like; being tested just after their memory chip had been inserted (I predict that to be a mistake of the scientists because the chip had not been fully adapted by their host, or just because Yi and the others are mentally justice). So this is how PROJECT members except Zed escaped, and Zed's mission is to track and destroy or capture them alive and bring them back to be programmed again.
After escaping laboratories of PROJECT, the members wonders around and discovers the PROJECT, they start to attempt to gather other members in an attempt to stop the PROJECT, like the video PROJECT:OVERDRIVE show, in which Yi is met up with Fiora and Lucian and battles against Zed who arrives on the news of Yi breaking out. After their battle, nothing more is revealed about them. Them all of the PROJECT members except Zed all meets up and start to stop the scientists. So, maybe Zed is dead after the battle, and they kill all the scientists, mission COMPLETE!!!! Or Zed survives and goes back to the scientists and urge them to produce more PROJECT, like Lee Sin and Varus(but the scientists definitely be more careful. Yi and his friends might die... etc. etc. There is countless possible thing might turn out for them......
You are free to think about what happens to them
I just like to write stories, hope you all liked my theory of the PROJECT.
