And if there is going to be a switch, then Mason needs to go immediately to LeBron, to prevent him from rolling to the basket. Which is what Mason did.
Mason misread the play: when Davis cut towards LeBron, he assumed a screen and acted accordingly. Davis, obviously, did not go tight to a LeBron screen, and instead went wide. But having called for the switch, Mason followed through, and Grant needed to to follow through as well. Mason was there covering LeBron, all Grant needed to do was take a step toward Davis--ready to cover a pass to Davis, and ready to help on LeBron.
So in the end, Mason misread the play, but Grant failed to execute the plan. Both are at fault.
And even then, Denver still got a hand up on the shot. And forcing a 3 in this scenario is better than giving up a look closer to the basket. So kudos to Anthony Davis for hitting a difficult shot.
As an aside, a huge pet peeve of mine in the last few years is teams taking long 3s when down by 1 (or tied). Any shot will win the game, and there's no bonus for margin of victory. Who cares if taking a 3 is a more efficient shot at other times in the game---at this point, get the highest percent shot, period. And usually, a mid range or shot in the paint has a higher overall chance of going in than a shot far from the hoop.