I would still try to sell LeBron on either the pipe dream Kobe + Randle + Melo + LeBron.... But there's a different pitch that they can make...
Theoretically if it goes down to what is reported in contracts, Heat will only have $5mil in cap space after Big 3 renegotiates. Then $5mil MLE. At least $2mil of either has to be paid to Haslem per year for 3 years. Either makes their starting lineup entirely the Big 3 again or mediocre bench again.
Lakers could give LeBron his max. Then sign Lowry to a bit over $7mil. Then have $5mil for MLE.
Same Roster in Miami will get slower and slower. But no flexibility in next 3 years, and 1/2 - 2/3 of the salary cap will rely on guys in their 30s, which will get harder at 33. Lakers give similar roster.... BUT can completely change entire face in 2 years. Can give him his choice.
Offer him his pick of coach.
And if LeBron takes less than the $22mil, more could be offered to Lowry, or another player or two on the bench.