Impiety = a break with nature. The programmatic opening of Book IX builds a single chain: every sin against one's neighbour, against truth, and against evenness is ἀσέβεια, impiety "toward the eldest of the gods" — the TERMnature of the Whole itself. The logic: nature framed DOGMArational beings "for one another — to help according to desert, not to harm" (the same formula as 8.59; 02-01) — so injustice violates her will (βούλημα) and is a sacrilege.
Lying as impiety: nature = truth. The second move is subtler: the nature of the Whole is the "nature of the things that are" (ὄντων φύσις), and it is also named ἀλήθεια (truth), the "first cause of all truths." Hence the liar profanes the same divinity. Two liars are distinguished: the willing (he deceives — therefore is unjust) and the unwilling (he is out of tune with nature, introduces ἀκοσμία, "disorder"): he has neglected the "starting-points" (ἀφορμαί) nature gave for telling true from false, and so is thrown off.
The chase after pleasure — impiety too. Whoever pursues TERMpleasure as a good and flees pain as an evil must blame the common nature (that it distributes "contrary to desert" to bad and good) — and to murmur at the ordering is impiety. Further: he who fears pain will sooner or later dread "something to come in the world," and he who chases pleasure will not hold back from injustice.
Indifference to what nature takes "equally." The climax is the Stoic indifference under the sign of piety: pain/pleasure, death/life, fame/dishonour nature "uses equally" (ἐπίσης) — and it would not have made both members of a pair without being evenly disposed to them. So DOGMA"the one who wishes to follow nature" must himself hold evenly toward them; whoever is unevenly disposed profanes. Thus the discipline of desire (ἀπάθεια toward externals) is re-described not as self-mastery but as piety: to fall out of tune with nature's evenness is to offend the god.
"Equally" = providence and the seminal reasons. The closing qualification: nature's "using them equally" means all befalls "in sequence" (κατὰ τὸ ἑξῆς) from DOGMAthe original impulse of providence (ὁρμὴ ἀρχαία τῆς προνοίας), which set out to the present ordering (διακόσμησις), MOTIF"having conceived the seminal reasons (λόγοι) of what was to be, and marked off the generative powers" of substances, TERMtransformations, and successions (cf. 04-14 — the return into the λόγος σπερματικός; 7.75). The governing discipline is desire (evenness toward the indifferent as piety), the sustaining one action (justice and truthfulness toward one's neighbour).