I would be willing to be that Lee ends up with a contract less than $65M over 5 years. Given the amount and talent level of the 2010 free agent class, I find it hard to believe that there will be enough $$$ under the entire league's collective salary cap to ensure Lee gets $12M.
This is an estimate of available cap space:
ATL-- $8M (assuming Joe Johnson leaves)
Bos --$0
Char - $0
Chi-- $18M assuming they non-tender Ty Thomas
Cle--$22M assuming Lebron leaves
Dal-- $11M assuming Dirk leaves... $22M if they don't pick up Howard's option
Den --$0
Det-$4M
GS- $2M
Hou- $16M
Ind- $0
LAC- $16M
LAL -$0
Mia- $48M assuming Wade leaves
Mem- $8M assuming they non-tender Rudy Gay
NJ $30M
NO- $0
NY $28M
OKC $15M
Orl- $0
Phi- $0
Pho -$10M assuming Amare leaves
Por $0
Sac-$14M
San- $0
Tor- $9M (assuming Bosh leaves)
UTA $0
Was -$2M
So, there are 9 teams that can offer Lee $12M or more without a sign and trade before accounting for 1st rd draft pick guaranteed contracts of at least $1M. I also didn't count cap holds and filler contracts. So actual cap space will be less for most teams.
After Lebron, Wade, Bosh, Amare, JJ, and Dirk all get max contracts, and then Boozer and Manu get high ticket contracts, I find it hard to believe that there will be many (any?) teams offering Lee $12M.
Keep in mind the state of the economy and the fact that the luxury tax is at $65M for next year. Teams like OKC will not be using that extra cap space to add much salary if they have any hope of keeping Durant. Cleveland without Lebron isn't signing Lee for $12M. Sactown maybe, but they have Hawes and Thompson. Clips have Griffin at PF, they aren't bringing in Lee. Houston has Scola and Landry. Really, that leaves the Nets and the Heat as realistic teams that might offer Lee $12M. I'd bet the Heat get 2 max FAs in Wade and Bosh and fill in the roster with the balance. That leaves the Nets (as you mentioned). But with the other available talent, I can't see them paying $12M for Lee when they have no other real competition.