Previous discussion on the site
This is a follow up to the question: In the time of Jesus, were the Jewish authorities allowed to execute? - the selected & most upvoted answer concludes:
The only ways a person could be executed were to obtain the imprimatur of the Roman prefect (the legal method) or gather up a lynch mob and do it yourself (the illegal method)
This does not, however, directly resolve the question of which method was employed in the death of Stephen, the legal or the illegal method? Was Stephen judicially sentenced, or was an angry mob riled up to do the dirty work without legal authority?
(Some interesting back and forth on the topic in the posts/comments of this question.)
The commencement of the trial of Stephen in Acts 6:
11 Then they suborned men, which said, We have heard him speak blasphemous words against Moses, and against God.
12 And they stirred up the people, and the elders, and the scribes, and came upon him, and caught him, and brought him to the council,
13 And set up false witnesses, which said, This man ceaseth not to speak blasphemous words against this holy place, and the law:
Stephen is taken before the Sanhedrin.
At the end of the trial of Stephen in Acts 7:
57 Then they cried out with a loud voice, and stopped their ears, and ran upon him with one accord,
58 And cast him out of the city, and stoned him
A mob of people is assembled (quickly?) to stone Stephen...but on who's authority?
At the trial of Jesus:
Then said Pilate unto them, Take ye him, and judge him according to your law. The Jews therefore said unto him, It is not lawful for us to put any man to death (John 18:31)
This is (maybe?) shown in practice in Matthew's account:
65 Then the high priest rent his clothes, saying, He hath spoken blasphemy; what further need have we of witnesses? behold, now ye have heard his blasphemy.
66 What think ye? They answered and said, He is guilty of death.
1 When the morning was come, all the chief priests and elders of the people took counsel against Jesus to put him to death:
2 And when they had bound him, they led him away, and delivered him to Pontius Pilate the governor. (Matthew 22:65-66, 23:1-2)
The Sanhedrin determines that Jesus should die, and they decide to take Him to Pilate to have their decision carried out (and endorsed?).
Statements by Josephus
Josephus reports the following words spoken by Titus to the Jews, regarding the sanctity of the temple:
Have not we [Rome] given you leave to kill such as go beyond it (Wars of the Jews 6.2.4)
Josephus also provides the following account of the death of James the brother of the Lord during the interregnum between Festus & Albinus:
But this younger Ananus, who, as we have told you already, took the High Priesthood, was a bold man in his temper, and very insolent....he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead; and Albinus was but upon the road. So he assembled the sanhedrin of judges, and brought before them the brother of Jesus who was called Christ, whose name was James: and some others...And when he had formed an accusation against them as breakers of the law, he delivered them to be stoned. But as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done. They also sent to the King [Agrippa,] desiring him to send to Ananus that he should act so no more: for that what he had already done was not to be justified. Nay some of them went also to meet Albinus, as he was upon his journey from Alexandria; and informed him, that it was not lawful for Ananus to assemble a sanhedrin without his consent. Whereupon Albinus complied with what they said; and wrote in anger to Ananus; and threatened that he would bring him to punishment for what he had done. (Antiquities 20.9)
Depending on how these passages from Josephus are interpreted, they may conflict with each other.
Was Stephen put to death by legal execution or a lynch mob?