I don't know when Lebron started lifting weights, but when you start lifting weights for a long period of time (I am talking about years here), your body starts elevating the levels of testosterone naturally, leading to more muscle mass. Theoretically, if a kid (11, 12 yrs old) started lifting weights for power (heavy sets), if timed right with puberty, those factors could result in a stronger, bigger person at an earlier age. However, this can't be proven since it's not advisable for young kids to lift heavy weights because it may disrupt with the growth of bones so there aren't many research on this.
However, this is more of a speculation more than anything. It's hard to tell if Lebron (or Oden) have used HGH, but I think the reality is that more muscle mass would result in a slower player and vertical leap would suffer. Also, most likely there would be more injury since the growth of muscles in certain areas would be out of wack (less likely if done naturally). I personally think that steroids works better in performances that don't need anything else besides quick power and strength (like sprinting, swimming, cycling- sports that doesn't need a lot change of direction besides quick powerful strokes). Although there have been some minor cases of steroids in basketball, but not nearly close to the NBA.
PS. All this information was based on my Diet, Supplement and Performance class.