The Lakers just gambled for Davis and traded their young players for him, and why would the Pelicans trade him? That's because of the said issue, he is prone to injury.
That's not the reason mate why Anthony Davis was sent to the Los Angeles Lakers:
a) Anthony Davis requested a trade and he shows interest to be part of the Lakers team. New Orleans Pelicans is
suc*s in surrounding Davis with a good bunch of role-player teammates for years that's why it just makes sense for him to ask for a trade.
b) Lakers just did a good job of trading their young players because having a young core seems not effective to them. The Lakers are playing with full young cores for several seasons and they didn't even make it to the playoffs until LeBron James came to the franchise. The Lakers are also taking advantage of LeBron's still on prime-performance that's why they try to acquire a Superstar-level to be part of the team and it's a timing that Davis wants to be a Laker. The Celtics even try to talk with Davis but he's not interested.