We flew Club World on BA from Heathrow to New Orleans last year.
With the exception of the arrivals lounge, all of them are after security.
There are two at either end of Terminal 5A, they are okay but nothing special, you'll be very lucky to get a spa treatment booked as most of them are pre-booked by first class passengers who get the option to book ahead, where as Club passengers can only book on the day of travel & in person when you get there.
There is a lounge in terminal 5B which is much nicer & quieter than the A lounges & provided your flight is going from a B or C gate I would recommend that you head over there as quickly as you can.
The food & alcohol choices are exactly the same in all of the lounges, if you fancy a glass or two of champagne you will have to flag down a server & ask them.
They should let you know whether your flight is going from an A, B or C gate when you check in.
If where you sit in the cabin is important to you then you may want to pay to pre-book your seats or you will be assigned seats which may not be together, they were using a 787 dream liner on that route last year which has two Club cabins (No first class), we booked seats which from memory cost us about £60 each so circa £220 out & back.
We booked a car to take us from the airport into New Orleans, we used the company listed on the airport web site, the driver was waiting for us with a sign when we walked out from the baggage claim area.
You'll have a great time in New Orleans, it's a fun town, if you want any more info on Club World or New Orleans, let me know.