LeBron James said he always knew if he became an NBA star, at some point in his life he would make sure the antiquated gymnasium at St. Vincent-St. Mary High School was renovated. Now the challenge could be sticking to his budget. The three-time NBA Most Valuable Player now with the Miami Heat has donated $1 million for a state-of-the-art gym at his alma mater that is slated for completion this fall. James has appointed St. V-M boys basketball coach Dru Joyce II to oversee the project for him, but Joyce said everything will be run by James. “He has some ideas, for sure,” Joyce said. James will be heavily involved, he said in a telephone interview Thursday evening as the Heat await the second round of the NBA playoffs. “I’m a hands-on guy and this is going to be more hands-on because it’s something that means a lot to me,” James said. “I’ll try to be hands on with Coach Dru, with the school, with the floor, the locker rooms, the bleachers. … I have a good sense of what stadiums or arenas or schools or gyms should look like.” But James agreed he might have more than $1 million taste. “I’ve got to keep it right there now. I’ve got to be responsible,” he said. “I told coach Dru, ‘We’ve got a budget. We’ve got to stay inside that budget.’ ” Planning started in January and renderings are under way for what will be named The LeBron James Arena. The project will include a new floor, lighting, bleachers, locker rooms, restrooms and an upgraded training room. One wall will tell the story of James and his high school friendships and “why he is so emotionally tied to us,” said Patty Burdon, St. V-M public relations manager.