Yep, it appears that MDC wanted to be caught for his infamy and perceived glory. His motive was simply that.
On the other hand, it appears that LHO had more than infamy as motive. Political ideology and revolution were apparently his main goals.
He went to his rooming house - showing no interest at all along the way as to what happened to JFK - changed clothes, got his loaded revolver and took five extra bullets. He shot Tippit. Tried to shoot it out at the theatre.
He was trying to go down in a shootout but was stopped. After getting caught he wanted the communist lawyer John Abt to represent him. Abt was known for putting the government on trial and that's what he planned to do: plead a victim of capitalism. He said numerous times throughout his life that he hated the American political and economic systems. I think he didn't expect to survive - which is why he left his wedding ring and nearly all of his money with Marina - but having done so he would play the victim card.
So his motives were probably - given his makeup - a mix of personal desire for fame, for notoriety and politics.
Or he was innocent and all of these people lied to frame him. People in the FBI and Dallas Police and CIA and waitresses and cab drivers and steamfitters and shoe salesmen and ticket takers and on and on and on.