Try checking LHR-LVI on ba.com to see availability. You can then select JNB as a stop over.

I did LHR-JNB-LVI a few years ago with a stopover both ways in JNB on miles (F for LHR-JNB and J for JNB-LVI. No extra miles required - same number of miles of JNB as for LVI via JNB since both are in the same zone.

Initial stopover in JNB was to relax and chill prior to LVI so that we could fully enjoy our time in LVI and make sure we had our luggage safely with us. Stayed at the Saxon House (who arranged the transfers) and is a world apart from the rest of JNB and South Africa. Fantastic service, great food, nice pool. They also provided us with a short transfer to the shopping mall and restaurants in Sandton (the only safe part of JNB). Hey - Oprah has stayed here along with Nelson Mandela. You cannot beat that for a reference. The normal rooms are really junior suites and the presidential suites are bigger than most flats! A really great way to start the honeymoon.

JNB-LVI in J gets you international lounge access through Comair. Its mainly tourist traffic in Y. On our flight, we were the only pax in J so it did feel like a private jet. Views on the left side of the plane gives a fantastic view of Victoria Falls.

LVI is a very small airport and is a interesting experience

We stayed at the River Club. Met by the owner at the airport the transfer to the hotel in part by road and the final bit by river (bags went on in the mini-bus). What an arrival! All rooms are individual split level villas with 3 walls. The missing fourth wall gives the wild outdoors experience (a noisy hippo kept us up one night). The right mixture of rustic and luxury combined. Meals are taken around one large dining table that fits in 20+ people so you meet everyone in the lodge and some of the staff. Food is reasonably good but you get the impression that the kitchen is using a cookbook from the 1950s/60s with items like a cheese souffle for starters (also used to be serve in CW at one time). Great to meet your fellow travellers/guest. Evening entertainment is just guest talking to each other but talent in our group meant we had a good sing-a-long one nice with a slightly out of tune piano.

River safaris are included in the price and sometimes given by the owner, Peter Jones. He is great story teller and guide. They also organise trips to Victoria Falls (taking tea on the island right at the edge on top of the Falls). We also went for an elephant trek at an elephant reserve - One person per elephant so it is not a kiddie ride. Definitely recommend all these trips

Returning from LVI, yes there is a BA lounge in LVI. Its the only lounge in LVI given how small the airport is.

If you want to do an open jaw with an Amex 2-4-1, then you have to ring BAEC.
A trip that is on miles cannot be on the same PNR as cash paid trip. It will be 2 PNRs.

Where exactly do you want to do the safari? Zambia does not have really good safari parks. The good safari parks are in South Africa Kruger (Sabi Sands area - the safari lodges organise charter planes from JNB not that expensive) and in Botswana (Chobe area). Again, use a JNB stopover and get a separate trip to either locations.

Unless you have a specific reason to visit Lusaka, I would you suggest you do go back to JNB with a second free stopover and arrange a safari trip from JNB. There are reliable internet firms like Go2africa.com or Rhinoafrica.com that can organise all the logistics for you but are happy with you arranging for your own air travel. SA have safari camps to suit all budgets. Botswana is not cheap.

PM me if you would like more info