Russell, a 19-year-old guard from Ohio State, was selected with the second overall pick in June. His contract is likely to total $23 million, starting at $5.1 million for the upcoming season.
Nance, son of former Cleveland Cavaliers and Phoenix Suns All-Star Larry Nance Sr., was taken 27th out of Wyoming via the Houston Rockets selection acquired by the Lakers in the Jeremy Lin trade last summer. The 22-year-old forward is under contract for approximately $5.9 million.
Only the first two years of Russell's and Nance's contracts are guaranteed. The Lakers have options on their third and fourth seasons, after which they're eligible to become restricted free agents.
On Thursday, the Lakers signed former Stanford star Anthony Brown to a three-year, $2.6-million contract. His first two seasons are fully guaranteed, despite his second-round status (34th pick).
The Lakers now have 14 players under contract, one below the regular-season maximum of 15; the franchise is likely to bring 17 to 20 players to training camp in October.
The contracts of Jordan Clarkson, Tarik Black and Jabari Brown are non-guaranteed at a minimum salary of $845,059. Clarkson and Black are locks to make the roster, while Brown might have to earn a spot before opening night.
The Lakers now have roughly $71.1 million in salaries, $1.1 million over the NBA's $70-million salary cap. The team also has a $2.8-million "room exception" to add to the roster, after which the Lakers will be limited to minimum contracts.