The team also renounced its rights to Johnson and Henry, along with Kent Bazemore, who has an unsigned agreement to join the Atlanta Hawks.
Confused? The salary guidelines in the NBA collective bargaining agreement can often seem counter-intuitive.
The Lakers need cap room to re-sign Nick Young to a four-year, $21.5-million contract. Even unsigned, both Johnson and Henry take up $915,243 of salary cap space.
By renouncing the pair, the Lakers gain an extra $815,814 to pay Young.
Johnson and Henry are expected to sign one-year minimum deals, both at $981,084. Their deals can be consummated after Young is re-signed, as teams over the cap are able to sign players for minimum contracts.
The details of Kelly's agreement with the Lakers are not yet known. As an unsigned restricted free agent he takes up $1 million of the team's salary cap space.
With Kelly's current offer, the most Young can earn over four years is $19.3 million.
The Lakers may need to revoke Kelly's qualifying offer and renounce him, which would then give the team just enough to pay Young $21.4 million over four years.
The Lakers probably would need to use some or all of their $2.7-million room exception to re-sign Kelly -- unless the second-year player is willing to return at the league minimum of $816,482.
Johnson, Henry and Kelly would have to sign after the Lakers exhaust their cap space on Young.
The Lakers also have a verbal agreement with Jordan Hill on a two-year, $18-million contract, which also won't be signed until after Young's deal is finalized.
Kelly averaged 8.0 points and 3.7 rebounds per game for the Lakers last season as a rookie, and he improved later in the season with additional playing time. Johnson averaged 9.1 points and 4.4 rebounds.
Henry is recovering from knee and wrist surgeries. He played 43 games for the Lakers, contributing 10.0 points and 2.7 rebounds a game.
Mike Bresnahan contributed to this report.