LBJ clearly refused to go along with the plotters' effort to use the assassination as an excuse to invade Cuba and/or to attack the Soviet Union. If he had been part of the plot, it's hard to imagine that he would have opposed that crucial component of the conspirators' plans.
LBJ learned that Russia had put it's nuclear bombers in the air immediately after the murder of President Kennedy. ( I'm sure that you know that JFK was communicating with Khuershev and Castor outside channels, And Nikita knew that John Kennedy was having trouble keeping the militant militarists at the Pentagon in line. Many were furious that General Cabell had got the axe after the BOP. The majority of them old war hawks had thought that JFK should have sent US forces against Castro at the BOP, and they also thought that JFK should have attacked Russian ships during the missile crisis in the autumn of 62. And then launched nuclear missiles against Russia. )
LBJ knew that Russia had the finger on the nuclear trigger.....so he didn't want any hint that the US was going to rashly blame the Russians for the murder of JFK as the old war hawks believed. LBJ KNEW that the Russians weren't involved.
On SaPersonay morning 11/23 63 Gordon Shanklin the FBI SAC of the Dallas office told the assembled FBI agents....Quote" Washington does not want any of you to ask questions about the Soviet aspect of this case. Washington was does not want to upset the public" the referral to "Washington" did not mean FBI headquarters, for Shanklin "Washington" was shorthand for the White House. Unquote From FBI agent James Hosty's book Assassignment : Oswald
Please understand that I doubt that the plot to murder JFK originated with LBJ..... But he was privy to the plot, because he had learned of the plot from J. Edgar Hoover, whose FBI agents had uncovered the plot. Neither Hoover nor LBJ did anything to foil the plot. They conspired to keep the plot secret and aided and abetted the plotters.
But the American militarists were thrilled that the Soviets had put nuke bombers in the air, giving them the perfect excuse to launch a full strike on Russia, but LBJ would have none of it.
Also, crucially, LBJ worked mightily to shut down Helms, Scott, etc., from publicly, and even privately, pointing the finger at Castro. Douglass covers this in some detail.
It is clear that the plotters planted evidence pointing to Castro in the hope of using JFK's death as an excuse to topple Castro. But when their media assets barely began to "reveal" this evidence, LBJ stomped down hard and virtually silenced such efforts. LBJ and Hoover also read the riot act to the CIA to stop pushing the narrative that Oswald was a Cuban agent and/or that Castro was behind the assassination.
Again, if LBJ had been part of the plot, he would have done all in his power to push the Helms-Phillips-Scott narrative, but instead he crushed it.