The old, original meaning of "bolt" was a "heavy arrow." For example, the arrows used in crossbows are called "bolts."
Lightning is a flash of light in the sky that occurs in an electrical storm. It is accompanied by the sound of thunder. When lightning reaches the ground it causes damage. We say that it "hits" or "strikes" something. We speak of an individual flash as "a bolt of lightning," or "a thunderbolt," or "stroke of lightning."
Cytowic's colleague is apparently experiencing synesthesia. He perceives the startling sound of his pager's alarm as red flashes. "Red lightning bolts" could either mean just some kind of red light, or perhaps it is literally a red, glowing, zigzag line."