There was an earlier Jew-Christian dialogue called Dialogue of Jason and Papiscus, written ca. 140, attributed to Ariston of Pella (or less frequently, Luke the evangelist). It was lost in antiquity, but it is thought by some scholars that Justin’s dialogue may have been influenced by it. Just a few fragments survive, including one excerpt discovered just a few years ago (François Bovon and John M. Duffy; HTR, 2012), which makes the interesting claim that the ascension occurred on a Sunday and the establishment of the kingdom of God would also occur on a Sunday (Urzeit-Endzeit concept, as Sunday marked the first day of God’s creation).
Timothy Horner wrote a good analysis of the subject:

“Over thirty scholars have been dealt with in this chapter and yet a consensus or even a pattern of opinion is elusive. Five categories of opinion [of Trypho’s historicity] can be discerned, yet even within each of these categories there is very little consensus between more than two scholars.”

Listening to Trypho: Justin’s ‘dialogue with Trypho’ Reconsidered