Well...I reckon LHO was ordered to meet his handler at the theatre after the assasination and the plan was for Officer Tippett to kill him before he reached there and it'd all be neat and tidy. Tippett, by all eye witness testimonies, was extremely anxious looking and acting very strangely before hand-barging into a music shop, asking to use the phone then leaving very quickly after getting no answer-he was well off his normal beat as well. LHO shot him, possibly in self defence, and, in panic, carried on with the plan to meet his handler who obv had no intention of being there. Only government depts could set that up-they then couldn't get to LHO when the local PD caught him(which wasn't in the plan) and used their mafia contacts to kill him within the PD-they gave Ruby the "offer he couldn't refuse" who said as much in testimony just before he died. None of that is far fetched....

Who shot JFK? LHO probably fired at least one shot, otherwise he'd have no real reason to panic, shoot a cop and still go to meet someone in the theatre(he wasn't there to watch a movie!) but I reckon government depts always had the final kill shots planned and LHO was, to some extent, the Patsy.