A traded-player exception can be used to acquire a player in trade without sending out matching salary. In the case of the Blake exception, the Lakers can deal for a player making up to $2,889,920 (including $100,000 of padding).
Given the NBA's trade deadline has elapsed, the Lakers won't be able to use the exception until after the season.
Technically the Lakers' trade with Golden State was broken into two transactions. Teams are able to acquire players making the minimum salary without salary matching, which enabled the Lakers to bring in Bazemore at $788,872.
The second part of the deal was Blake being swapped directly for Brooks. The difference between Blake's $4-million salary and Brooks' $1.2 million is the newly generated trade exception.
The exception expires on Feb. 19, 2015, but the team may not have it for long. Should the Lakers drop under the salary cap in July, as expected, they will first need to renounce the exception.
Once the Lakers are under the cap, they can acquire players without matching salary -- so long as the team remains below the cap upon completion of the deal.
The Lakers might find a use for the traded-player exception around the NBA draft in June, but to do so, they'll have to be willing to take on a player under contract beyond the current season.