Best way to take Lion Pictures close-up is driving around in a vehicle. If you go on foot most Lions will run away! However if they come close you might be the one jumping into a tree!
Best game parks in Southern Africa are within Botswana , Chobe National Park (the Savute area) and Moremi Game Reserve. You will find large prides of lions 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 camera 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).
Other game parks like the Kruger National Park (South Africa) are also nice for game viewing. In Namibia there is the Etosha National Park. And in Zimbabwe the Hwange National Park and the Mana Pools National Parks are the best places to take Lion Pictures.
In general Lions will not attack a car but the may come very close and touch the vehicle and/or start mauling the vehicle tires. Be aware!
Lion Picture lenses
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.
You can always take nice pictures of Lions with your iPhone. In particular live images will be nice. But do not use a flash as the light will scare off the Lions.