I don't think Lex was convicted actually. Didn't Superman fail to show up to the testimony? He was charged but not convicted.
And to testify for his innocents regarding the events of SR, Superman claim Lex had no part in it. To Lex's surprize, Superman let him free, twice, or so he thinks. When he returns to the Vanderworth residence he discovers the crystal in to little train set has grown, and that Brainiac's essence is in it, talking to him.
Brainiac made a Superman clone to set Luthor free, (this clone always lies (but in a subtle way), and eventually becomes Bizarro. (the backwards "S" will come when he is deteriorating and see's a reflection of himself, with the backwards "S", so he takes it off and wears it inside out). Before Bizarro turns ugly, he'd take down Richard's airplane, (out of envy) and presumably kill Richard.
Superman doesn't know how to explain what has happend, So as Clark he tries to write something to clear his image, Lois goes crazy (having lost her husband) and tries to beat up Superman, Superman tells her his true identity.
Back to Luthor and Brainiac- Brainiac helps Luthor develop arms and high powered missiles and thus he gets his Lexcorps started.
In the end Lois admits her love to Superman, Bizarro and Superman duke it out, people realize why "Superman" was acting crazy, Brainiac launches a bunch of LexCorps nukes, Bizarro sacrifices himself to stop the world. Metallo breaks Lex out and goes after Superman, Jason save's Superman from Metallo (aka Richard) and Brainiac is "destroyed."