I'm sure they would. But the Suns wouldn't.
That's probably why Kawhi's camp have left it this late to meet with the Spurs. W're now down to less than 40 hours before the draft, there's simply just not enough time for the Suns or the Kings or any other teams to have a medical team clear Kawhi and they would be reluctant to pull the trigger on the trade.
Lakers don't have a decent draft pick so their position is gonna be stronger after the draft than before it.