Well, I'll tell you the ones I know of.
Shops (that don't have a lounge):
Vendome Liqours, Toluca Lake (corner of Riverside & Cahuenga). My favorite.
Vendome Liqours, Studio City (on Ventura Blvd.)
Shops with a lounge:
The Big Easy, Studio City (on Ventura Blvd.)
The Cigar Warehouse, Sherman Oaks (on Ventura Blvd.)
Fat Stogies, Encino (on Ventura Blvd.)
Havana, Studio City (off of Ventura Blvd.)
The Brand Cigar Club, Glendale (on Brand)
there's a few more in Burbank/Glendale I know of, but can't remember the names, and they're rather small joints.
There's also a shop in Santa Monica on Broadway near the 3rd St. Promenade, but I haven't been there in a while. They have a lounge as well.
And finally, there's the famous Tinderbox in Santa Monica (or is it Beverly Hills?) which I've never been to but have heard it's like a landmark. It's on Wilshire Blvd. I believe.
Luckily for us, LA is full of smoke shops. I usually spot one I'd never seen before every week! Alas though, my Wednesday nights are busy playing hockey. Maybe some other time. Good smoking and I hope you enjoy your stay!
P.S. You gotta try a double-double from In 'N Out at least once. Preferably "animal style".