There's not really any good solution unless you have a player who can guard LeBron one-on-one, and even then you can't expect to shut him down totally or prevent switches that put him in favorable matchups. It's a problem every team going up against LeBron in the last 7-8 years has faced. He's just a walking mismatch and he doesn't have any real weaknesses.
You have to hope he's fatigued, playing at half-speed, or just plain bored to have a chance.