Jake doesn't have to kill Oswald...
He just has to alert Secret Service that there's a sniper intending to aim at JFK inside Dealey Plaza...they might think Jake is just a crazy person at first, but they'd probably at least stop or turn the motorcade around, search Dealey Plaza, and find Oswald there with his gun, at which point they'd apprehend him. Jake still saves the day, and doesn't go to jail...because you got to think that if Jake follows through with the plan to kill Lee Harvey Oswald before Oswald assassinates JFK, they're probably going to arrest Jake for murdering Oswald and conclude that they were accomplices in intending to kill the president, but their relationship soured, so Jake's going to serve multiple life terms for murdering Oswald and conspiring to assassinate the president...Plus, they're going to find out about him killing Frank back in Kentucky, and that whole thing with Sadie's ex is going to resurface. And since it's Texas, they're probably going to give him the chair or hang him. He'll never get back to the portal in Lisbon, Maine before police catch up with him...he probably won't even make it out of Dallas!
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