The LRA is a weird rebel group. Since it was pushed out of Uganda in 2005, the group has spread itself over thousands of square miles and over three countries (Uganda, Sudan and CAR). It has gone from being an almost entirely Acholi group to one where most of the footsoldiers are now Zande. According to accounts from researchers working on the LRA, the rationale behind their incredibly abusive behavior is partly internal: As they don't have a clear ideological program (at least not one that can attract recruits) and most of their soldiers are abductees and now no longer even from the same ethnic or linguistic background, they need violence as a way to socialize and indoctrinate their soldiers. Killing, in other words, often does not happen in response to contested military authority, but is used as a way make obedient soldiers.
(Other motives could be: using violence as a way to intimidate locals to provide them with resources and sending a message to foreign actors that the rebel group is strong and ruthless.)
Peace talks broke down when Joseph Kony refused to sign a deal in 2008 - satellite phone intercepts indicate that he has no intention of handing himself in. Most advocates I have spoken to, be they from governments, human rights groups or the UN, think that Kony will have to be killed to bring an end to the violence, although human rights groups have a hard time saying this in public. Some advocacy groups think that sending an international military force could set a good precedent for the execution of ICC warrants (Kony was the first indictee of the ICC).
International intervention may finally be in the cards. US Congress (which has been in a frenzy of Central Africa-related legislating) passed a bill in May this year requiring the Obama administration to support military and diplomatic efforts to deal with the LRA. The State Department is required to submit a strategy for this by the end of November. In private, US officials are skeptical about sending troops, but there have been suggestions that they could provide intelligence (they already do some of that) and financing for other countries to send in special forces.
In the meantime, Kony might be eyeing to get more support from Khartoum, a former ally who used to back him when it was at war with the SPLA. LRA troops have recently crossed into Darfur from CAR, and a defector suggested that they met with Sudanese officials there. As Sudan heads towards its all-important referendum on southern independence next year, a mercenary job or two might open by for the LRA.