Should “lifestyle” be plural here?
Solution 1:
Either one works syntactically, but there is a semantic difference. I would ask this question: Do the leaders each have their own traditional lifestyle that differs from the others? Or do they all have basically the same shared traditional lifestyle?
Using plural "lifestyles" implies that there are various lifestyles that they want to preserve, as long as they're all traditional. Using singular "lifestyle" implies that they are interested in preserving only one (very narrow or specific) lifestyle.