Given the necessity, a lion might kill or even eat a cougar, but these two big cat species don't share a habitat. Cougars are common in North America where there are no lions. Lions are common in Africa where there are no cougars. So, there is little possibility of these two animals coming face to face in conflict.
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If given an opportunity yes but they both live in two totally different continents and hence a lion eating a capybara is not possible.