I would like to know more about Rutherford's claims and the lightnings.
In his "Birth of the Nation" article from 1925, Rutherford interpretation the "lightnings" in the temple in Revelation 11:19 as new understandings of truth given to God's organization after Jesus came into his temple in 1918. So when Rutherford introduced a new teaching or understanding, he often described it as revealed by Jehovah's "lightnings".
"Since the Lord came to his temple there have been flashes of lightning; that is to say, intermittent illuminations of the Word of God, giving further glimpses of truth in his great plan. These flashes of light do not emanate from any member of the temple class, but from the Lord. It is Jehovah who is sending out his light and his truth, and at the critical time for the church" (1928 Yearbook, p. 201).
"JEHOVAH's lightnings now make it plain that the periods of time mentioned in tile Scriptures as "the day of his preparation" and the time of "preparing the way before the Lord" are not the same. In his own due time God sends his beloved Messenger to prepare the way before him. (Mal. 3:1) That period of time began about 1878 and continued until 1918, and there ended" (Watchtower, 1 November 1929, p. 323).
"Former things concerning God’s purposes that did come to pass were understood after the Lord came to his temple and the lightnings of Jehovah illuminated his Word. This same class then see new things which God has declared. In the light of prophecy in the course of fulfilment, and of the further illumination thereof by Jehovah, the remnant class is permitted to see other things that are shortly to follow, concerning which the Lord says: 'Before they spring forth I tell you of them.' Jehovah takes the remnant into his confidence in a measure by revealing to them the precious things that are in his keeping. These have a better understanding than ever before of what the great battle of God Almighty will mean and how Jehovah will vindicate his name" (Watchtower, 1 January 1930, p. 7).