Well, according to that thesis I cited ...
OK, let's first agree the ground.
The root question:
Was Arius a distinguished scholar of Lucian & Origen or not?
Impossible to say, because we can't reconstruct the theologies of Arius, Lucian or Origen to your satisfaction.
Do you agree?
..so we know what deviations (if any) Arius was actually propagating.
But you say we cannot reliably reconstruct Arius' theology.
Do you agree?
For the benefit of others:
It's unlikely Arius actually attended the school at Alexandria, but he lived and worked there, and would have been well aware of Alexandrian exegetical methodology. However, he claims his tutor was Lucian, who might well have been the first head of the School of Antioch, and the two schools adopted very different approaches, what bearing that might have on Arius' Alexandrianism is hard to determine ...
Origen would certainly have been an influential figure in Arius' time, but Arius does not accept Origen's idea of the eternal generation of the Son
, so we can assume Arius opposed Origen on that issue. Nor does Arius argue from any authority – he mentions some names with whom he associates as Subordinationists, and he mentions others, for example Emanationists, whom he repudiates as heretics, as did the orthodox church.
According to Ilaria L.E. Ramelli, (Professor of Theology and endowed Chair at the Angelicum, Rome, Humboldt Fellow at Erfurt University, Fellow of the Royal Historical Society, Honorary Professor at Durham University, Senior Member at the Cambridge Centre for the Study of Platonism, Senior Research Fellow at Durham, Oxford and Princeton universities!) –
Origen was a primary source of inspiration for the Three Cappadocians, as they were called, Basil the Great (330–379) bishop of Caesarea; his younger brother Gregory of Nyssa (c.335–c.395) bishop of Nyssa and a close friend, Gregory of Nazianzus (329–389) Patriarch of Constantinople (Cappadocia is a region in Turkey), who became the champions of Trinitarian orthodoxy.
Origen inspired Marcellus, who was anti-Arian, and notably Athanasius, so it's hard to place him as any way an inspiration for Arius, and he definitely would have opposed Arius insistence on the idea that 'there was a time when he was not'. Traditionally Origen is said to have been a subordinationist, but that is now under review by later scholars, to place his views in the context of his time and general theological development.