His coach, Phil Jackson, said Odom has been "invaluable" to the team.
When Odom was a free agent, Jackson urged the organization to re-sign him. The Lakers and Odom agreed to a four-year, $33-million deal in July 2009.
Otherwise, the Lakers might not be back-to-back champions and be talking seriously about winning a third straight NBA championship, Jackson said.
"We made a decision as an organization two years ago to sign Lamar, which put us in a difficult [salary] cap situation," Jackson said. "Yet we're convinced that without him, we wouldn't win a championship again. That was a good decision by the organization."
Odom has started 33 games this season for the Lakers, and played in all 70 and he has made a seamless transition between starting and being the sixth man.
He started again Sunday in the win over Portland and will start again Tuesday night against Phoenix while center Andrew Bynum serves the second of his two-game suspension for a flagrant foul.
All Odom did against the Trail Blazers on Sunday was produce a double-double with 16 points on eight-for-11 shooting and 11 rebounds. He also had six assists.
He is third on the team in scoring (14.3), third in rebounding (8.7), third in assists (3.0), second in field-goal (53.8%) and three-point (38.3%) percentage and third in minutes played (32.2).
"I know my role on this team," Odom said. "Now more than ever, I try to keep myself prepared just in case. Who knows? A turned ankle or a two-game suspension. Who knows what it's going to be? I just try to be prepared physically and mentally, just having myself in that good space where I can just come in and do a good job."
Maybe some good will come out of Bynum serving a two-game suspension, Jackson said.
Bynum said last week that he still has fluid on his right knee, the one he had surgery on last July.
He won't have played for six days when the Lakers face the Clippers on Friday night.
Bynum is not allowed to be in the arena on game days while on suspension, but he did practice Monday. He didn't talk to the media.
"He knows it's to his advantage … to have an opportunity to work on his leg strength and get some things back," Jackson said. "So I think this in the long run might help him."
Bryant on Fisher
In the three seasons point guard Derek Fisher was away from the Lakers — he played two years with the Golden State Warriors and one with the Utah Jazz before signing with L.A. in 2007 — his ability to knock down clutch shots was missed by Kobe Bryant.
" … I was throwing it to Smush" Parker, said Bryant, referring to the wayward point guard who played two seasons with the Lakers. "I shot with three [defenders] on me. That's the difference [with Fisher]. Now I only shoot with one, maybe two."