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I was wondering whether it is possible to establish a "Gini Index" for the Roman Empire or as a matter of fact for any of the late Empires?

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Yes, actually, many scholars have done an estimate of GINI index for the Roman Empire, even at different times, since the society changed a lot. It is commonly considered that inequality peaked around 1st century AD.

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For analysis on more societes, see Economic Inequality in Pre-Industrial Times

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    Looked a bit into that graph. Its available at the linked website. According to that source it "may be under copyright", and appeared to be uploaded by Guido Alfani. That's the name of a researcher in this field, so there's a good chance its Alfani's work.
    – T.E.D. ♦
    Commented Sep 29, 2022 at 17:56

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