One of the better turners at my woodturning club demo'ed turning boxes yesterday. He made three in under one hour, sans sanding. Still much faster than most of us could do.
His technique is simple and I learned how he makes the lids fit very well with little work. In a nutshell, decide where you want the lid to go, part down, part off leaving the small section (tenon) on the lid, turn inside of box and lip to where the lid tenon fits tightly.
BTW, his name is John Kincade. He can turn the tiniest, prettiest little spindles you have ever seen. Big guy with huge hands but a delicate touch.
Shown is a walnut box I made recently, pre his demo. What looks like a finish flaw is actually in the wood.