He was injured on a mission to Earth to stop the Blast Masters. Khyber almost killed him, but the other Magisters stopped him before he could do so. Paradox then took Lotin to the Infinity Pool. This was revealed in Mid Term, Part 2.
Why did Lotin agree to bring new recruits to the Plumbers' Academy?
He wanted to train them himself, as he said in Comprehension.
The crystal is used to open a door within the Temple of Rigon that leads to the Infinity Pool. The crystal can then be bathed in the pool to give the wielder and anyone else the wielder chooses the powers of time travel, space travel, immortality, immunity to disease, and more, as revealed in Unit Test.
He was kept sage on Ranova until he eventually broke free. Several recruits went to Ranova and encountered him. They were eventually able to cure him using the Shuffler. All this happened in the season two episode Time Bomb.
Why did Sci need to release dark energy into the Solvens Tenebrae Vestibulum and what is his secret?
In Cheaters, Lucifer mentions that Sci is the Child of Darkness told of in an ancient prophecy within the Solvens Tenebrae Vestibulum. Because of this, he has to release dark energy every so often.
Why does Sci only trust Paper with his secrets?
Also in Cheaters, Paper reveals that Sci trusted him because he had become friends with him, and needed his help once when he was away from his locker and needed to release some dark energy. It was confirmed by the creator after The Guardian that Sci subconsciously knew Paper was the Guardian, which is why he trusted him.