Justin evidently does not acknowledge the ontological equality of the Father and the Son of the Holy Spirit. To the contrary, he apparently makes a sharp demarcation between the Father and the Son in Dialogus cum Tryphone 127. Fortman adds that Justin: "has no real doctrine of the Trinity, for he says nothing of the relations of the three to one another and to the Godhead" (47). Additionally, he most certainly comes nowhere near affirming the famed VERE DEUS of Chalcedon or homoousion to patri of Nicea.
Finally, in a book edited by Nigel M. de S. Cameron entitled The Power and Weakness of God: Impassibility and Orthodoxy (Edinburgh: Rutherford House, 1990), Peter R. Forster also informs his readers that "the textbooks are widely misleading" when it comes to explaining the pre-Nicene LOGOS theory since "To take the case of Justin, with but few exceptions (1 Apol 59 (?), 64; 2 Apol 6) he attributes creation entirely to the transcendent 'Father of all'" (page 30). Forster also has other perceptive observations that I encourage you to read for yourself. He demonstrates how Justin is laboring under Middle Platonic and Stoic philosophical conceptions.