Lenny Dykstra -- Free to Watch Phenom Son Crush Baseballs

Lenny Dykstra's baseball stud son will now have a famous fan in the stands -- TMZ has learned, a judge just granted Nails' petition to get some time off house arrest ... just to watch his 16-year-old boy play ball.

According to the docs, obtained by TMZ, Lenny is now permitted to leave his CA residence to attend his son's remaining baseball games this season -- but there are rules ... Dykstra must get prior approval before each game he plans to attend.

Dykstra's son Luke -- a high school sophomore -- is a baseball superstar, who batted .383 with 29 runs, 15 RBIs, 10 doubles during his freshman year. He was also named to the MaxPreps.com Freshman All-American team.