Not exactly a "big band" date (lots o'strings), but this one is a mostly a gem afaic:
Never mind the "orchestra conducted by Frank Sinatra" crap. Maybe he did, maybe he didn't, whoknowswhocares, etc. What you got here is Lee singing ballads, great ballads, with arrangements by Nelson Riddle, who turns in some of his most harmonically devious work here. The version of "HAppiness Is Just A Thing Called Joe" is earfuck enough, but there's more...
Plus, Lee sounds like she's in some kind of wierd, channelling Billie Holliday mode here. Kinda creeped me out at first, but the arrangements drew me into the total package, and now I'm hooked.