Many critics of the Libya war, as was the case in the Iraq and Afghanistan wars, are seeking to explain the empire's motive by looking at what the target country has (especially natural resources), which the empire might want to have, and what the target country does, which the empire might want to stop.
In my view, rather than trying to explain each case of the empire's military invasions with ad-hoc explanations, it's better to emphasize as a given the fact that within the power elites of the Western powers, especially the United States, there is an influential bloc that is constantly advocating military "solutions" to states that those power elites regard as "problems." Let's call them "militarists."
The rest of the power elites, sometimes called "realists," also generally share the same goal -- regime change -- as militarists but they prefer "soft power" (support for in-country and in-exile "civil society" opposition + propaganda), economic sanctions, covert actions, military coups, proxy wars, etc. to the direct use of their own armed forces (mainly due to concerns about political and financial costs).
Sometimes the militarists get their way as in Iraq, Afghanistan, and Libya; other times they don't, as in Cuba, Iran, Syria, North Korea, etc. so far in recent decades. The difference is that the latter are tougher nuts to crack, for various reasons (such as the strength of the spirit of independences, the extent of political cohesion and the depth of ideological commitment, the number and power of international allies and supporters . . . and the demonstrated possession of nuclear weapons in the case of North Korea in particular). In other words, the question to be asked is which state in the South enjoys the power of deterrence and which doesn't.