All NBA players on nonguaranteed contracts become locked in if not placed on waivers by the Wednesday deadline.
Ellington is under contract for $1.1 million, of which $581,692 is guaranteed. Price's contract is $1.3 million, with $658,405 guaranteed.
Black, who was claimed off waivers from the Houston Rockets in late December, is earning a nonguaranteed rookie minimum of $507,336. He's also under contract next season, at a nonguaranteed $845,059.
If the Lakers keep all three, the team's payroll will lock in at $70.2 million for a full roster of 15 players, barring a trade.
The franchise recently waived injured swingman Xavier Henry (Achilles' tendon), despite his $1.1-million guaranteed contract, to make room for Black.