He wrote a great work on the doctrines of the Pythagoreans, and tried to show that the successors of Pythagoras had made no additions to the views of their founder, but had merely borrowed and altered the phraseology.
According to Plutarch's description, Lucius adhered to the rules of the Pythagorean way of life, so he valued the practice of a lifestyle oriented towards philosophical goals.
It is unclear whether this is due to the influence of his teacher Moderatus and thus no concrete conclusions can be drawn about his adherence to this lifestyle.
Another Moderatus fragment is preserved in Simplicius's commentary on Aristotle's Physics, which is taken from a lost treatise by Porphyry on matter.
[4] Moderatus wrote a work titled "Lectures on Pythagoreanism" in either ten or eleven books, which Porphyry characterized in his Life of Pythagoras.
Number one denoted to them the reason of Unity, Identity, Equality, the purpose of friendship, sympathy, and conservation of the Universe, which results from persistence in Sameness.
After all these methods were not confined to the Pythagoreans, being used by other philosophers to denote unitive powers, which contain all things in the universe, among which are certain reasons of equality, dissimilitude and diversity.
The Pythagoreans affirm that Plato, Aristotle, Speusippus, Aristoxenus and Xenocrates; appropriated the best of them, making but minor changes (to distract attention from this their theft), they later collected and delivered as characteristic Pythagorean doctrines whatever therein was most trivial, and vulgar, and whatever had been invented by envious and calumnious persons, to cast contempt on Pythagoreanism.A difficulty in determining the doctrines of Moderatus arises from the fact that Porphyry does not indicate exactly where in this account the rendering of Moderatus' statements begins and ends.
Another problem is that Porphyry may have inserted or altered individual passages of text, so that it is to be expected that in his account Moderatus' way of thinking and terminology appears more neoplatonic than it actually was.
Subsequent philosophers such as Plato, the Platonists Speusippus and Xenocrates, and Aristotle and Aristoxenus would have done no more than assimilate the fruitful contents of the Pythagorean doctrine, making only minor changes.
[5] Moderatus understood the Pythagorean theory of numbers as an attempt to communicate statements about metaphysical circumstances in a catchy language for didactic reasons.
[3] There it is said that Pythagoras showed his students a path to happiness by leading them in small steps from dealing with the material and perishable to contemplating the incorporeal, imperishable and real.
[7] Moderatus expressly does not allow sense objects to participate in the transcendent One and in the intelligible world, but regards them only as a reflection of ideas.
In a study published in 1928, Eric Robertson Dodds put forward his hypothesis that the ontological model of Moderatus is the result of a metaphysical interpretation of statements in Plato's dialogue Parmenides and that the Neo-Pythagorean metaphysics anticipate elements of Neo-Platonic thought (especially the Neo-Platonic Parmenides interpretation).
[8] This view has found favor in research, although the formulations handed down by Simplicius may not have come in part from Moderatus, but from the reporter Porphyry and reflect his neo-Platonic ideas.