Most of what I know about Lex's kids I used in
Missing Lois -- in which Jaxon plays a major role for a while -- and then I promptly forgot. I don't think I wrote it down and it would take a bunch of looking through dusty notebooks to see if I wrote any of it down. Let's see what I can recall from the top of my head...
From Virtually Destroyed: /
http://loisandclarkarchive.com/ThirdSeason/VD/vd08.htm / Fourth picture in - second row (since we can't link the actual JPGs from that site) has Jaxon Xavier's bio from "data net". He's 5'4", born Nov. 12, 1962 (which makes him about 3.5 years older than Clark). His mother and Lex were never married, but apparently Lex knew Jaxon was his illegitimate son. Needless to say, Jaxon had major daddy issues because of never being "claimed" by Lex.
Lex Jr did come from a legit marriage with Lex Luthor. Apparently his mother died in a car accident. I think. I don't know if Lex Jr was in the car at the time, which is how he got disfigured (maybe Mrs. Luthor was trying to escape Lex and took their son with her?). I vaguely remember Lois saying something of the sort when Luckabee came on the scene. Anyway, Lex Jr. was raised in Australia (apparently, though only Luckabee, the actor hired by Lex JR had the accent.) I don't know if Lex Jr was supposed to be older than Jaxon or not.
Lex was married to Arianna Carlin during a shipboard marriage 10 years before Lois and Lex were supposed to be married (roughly 1984, I guess). We never learned how long they were married or if Ari had any children with him, but it's always possible.
In the comics canon, Lex had an affair with Alice and was the actual father of
Jerome "Jerry" White (which would explain... other than his lack of father-time with Perry... his ending up in upstate prison for check fraud / writing checks that didn't belong to him and trying to kill Superman using Red K.).
Due to Lex's love of the ladies, I always assumed that he had more children than we had a chance to meet in the 4 short years of LnC. I even suggested another name in Missing Lois... Let's just say that Lex Jr had a twin sister.
