Excerpt from Sports Illustrated, June 18, 2012:

“34.3”

LBJ

LeBron James’s scoring average in his three game 7s (including 31 last Saturday against the Celtics), the highest in NBA history of anyone who’s played at least two such games.

The others:

Cleveland Cavaliers at Boston Celtics May 18, 2008 (45, L 92-97)

Cleveland Cavaliers at Detroit Pistons May 21, 2006 (27, L 61-79) (Gotta love those Pistons scores.)