Lamar Odom is the Lakers third most important player. He is the teams X-factor. For the most part, the team knows what to expect from Kobe and Pau Gasol.
When Odom was on, the Lakers were unbeatable. When he was not, they looked mortal. The Lakers blog Forum Blue and Gold (http://www.forumblueandgold.com/2009/06/19/cant-lose-situation/) has an excellent piece on what Odom brings to the team.
The overriding theme of the story is that the Lakers need Odom, which is true. Luckily for the Lakers, Odom should not be offered an enormous contract from another team. He is easily worth the full mid-level exception, which the Lakers clearly would beat.
Odom has stated his preference is to remain with the Lakers, so this eliminates any teams over the cap from swooping Odom. The only team that could potentially soil the Lakers plans is the Detroit Pistons.
They are the only contending team with cap space available. However, they are rumored to have offered Ben Gordon $11 million a year, and are also rumored to be hot on Hedo Turkoglu.
The only other teams who could offer Odom anything more than the mid-level exception are not serious contenders. Odom should eventually re-sign, for around $10 million dollars a season. He is easily worth it to the Lakers.