You don't need the military to resolve this: strengthen the International Criminal Court and criminals like Kony will get what they deserve without the need of armed forces.
It can, if Uganda and the DNC find a way to get their hands at Kony - while he probably has a good hideout, I don't think he's untouchable. Plus, some countries in the area, like Sudan, are not ICC members (in fact, al-Bashir was actually helping the LRA), and some others, like Kenya, have already their legal obligation to surrender wanted people before.
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