Cyril Lucaris was executed for treason by Sultan Murad IV, is there any evidence that members of any church were directly involved?

The subject of the "calvinist" Patriarch of the Orthodox Church comes up from time to time, with the 2 sides presenting conflicting versions of events. Here is what I am certain of already. 1. Lucaris was viewed as having heretical beliefs as viewed by the rest of the Orthodox Church at that time. 2. There was a tension between the Orthodox, Catholic, and Protestant faiths. 3. There were other ottomans who didn't like Lucaris. The Execution was deceptive from the start, as Lucaris was taken away as if to be banished. But later out of sight of the majority of people they strangled him with a bowstring. --- #### Question: Are there any sources or evidence that indicate one of the 4 parties mentioned were directly involved? Reason: A common assertion is that the orthodox church was attempting to remove him at "any cost", though I can't find evidence to support that.