Best way to take Lion Pictures is driving around in a vehicle. Best game parks in Southern Africa are within Botswana , Chobe National Park (the Savute area) and Moremi Game Reserve. You will find large prides in Botswana . Using for example a Land Rover 4×4 will take you close to the lions and will make it easy to take pictures. Best lenses anything between wide angle and 300mm. A larger lens should not be necessary as lion will come close to you vehicle. There have been several occasions I would have been able to touch the lion out of the vehicle (not recommended)
The picture above has been taken by using a 400mm lens. The Lion Picture below has been taken out of the driver’s seat of the Land Rover. The big male lion walked by and due to the size of the lens I could not get it 75mm a full picture of the lion. But as you can see this image is much more dramatically (being a close up) than a full image would have been.