RE: Help with ideas
From what I know, in your price range I do not think you would be happy with what you can purchase from the store for what you want it to do.
It sounds that you want to catch (get pictures) of the lions when they are getting chased, so you will need an extreemly fast trigger time, even if the camera has a wide angle detection cone. Most of your comercial trail cameras, even the expensive units will not react in enough time to catch the animal before it passes range when they are moving quickly. Some will not even catch the whole animal when they are walking before they walk trhrough the camera area.
I personally would save my money to get a better unit, or get a custom made unit for the purpose you want (home made are usually cheaper in costs and better in quality).
Hope this helps you.