Is the pouring of lac in a Shudra who hears the Vedas or recites them intentionally Danda or Prayaschitta?

Question

Generally, people say that Shudras who hear the sacred knowledge (Vedas) have to undergo painful punishments, but is this self-imposed or imposed by a ruling or governing authority? Because, if it is self-imposed, then it's more of a penance of sorts be it a painful one.

Answer 1

The OP is referring to Gautama dharmasūtra (2.3.4)-

atha hāsya vedamupaśṛṇavatastrapujatubhyāṁ śrotrapratipūraṇamudāharaṇo dhāraṇe śarīrabhedaḥ //

Here, severe daṇḍas are stated for the Vedaśravaṇa, Vedoccāraṇa and Veda vicāra & grahaṇa, done by Śūdras. But Vedaśravaṇa can be done by someone even unintentionally, say passing casually through a group of Brāhmaṇas doing svādhyāya, yajña, etc. Would such Śūdras be daṇḍita in the same manner as Gautama enjoins?
No, only buddhipūrvaka śravaṇa (usually done samīpa dvijas) is a doṣa, and not śravaṇa of mere dhvani of Vedavākyas by say chance, accident, negligence, etc. This is clarified succintly by nibandhakāra Śeṣakṛṣṇa and bhaṣyakāras Haradatta and Maskari, and quoted as follows -

asya śūdrasya upasṛtya buddhipūrvaṁ śṛṇvataḥ / tena dhvanimātra śravaṇena doṣa iti kecit / ~ Śeṣakṛṣṇa's Śūdrācāraśiromaṇi (p.42)

upaśrutya buddhipūrvamakṣaragrahaṇamupaśravaṇam / ...
upaśravaṇaśabdena yaddṛcchayā dhvanimātraśravaṇe na doṣaḥ /
~ Haradatta's Mitākṣarā bhāṣya on Gautamadharmasūtra (2.3.4)

haśabdo buddhipūrvasūcanārtha / ..upaśabdena samīpacācinā akṣaraśravaṇa eva doṣa iti darśayati / tataśca / dhvanimātraśca varṇe na doṣa / haśabdena buddhipūrva eva daṇḍavidhānāt pramādāt kadācidakṣaraśravaṇe'pi doṣābhāvo dṛṣṭavya /
~ Maskaribhāṣya on Gautamadharmasūtra (2.3.4)

Now comes the question, are the daṇḍas stated here by Gautama actually daṇḍas or not literal? Although this smṛtivākya states severe daṇḍas for Vedaśravaṇa, etc. by Śūdras, but it shouldn't be interpreted in a literal manner, in the sense that the Rājā is really enjoined to daṇḍita such Śūdras. In Brahmavidyābharaṇa (1.3.38), that is Advaitānanda's comm. on Bhagavatpāda's sūtrabhāṣya, where the niṣedha on Vedaśravaṇa, etc. by Śūdras is stated, Svāmī Advaitānanda clarifies that the above stated smṛtivākya (by Gautama) is pratyavāyabodhaka (trapujatubhyāṁ sīsalākṣābhyām ... udāharaṇe-vedasyoccāraṇe / ...nanu-śūdrasya tato'pyadhyayanaṁ satsvapi, teṣāṁ pratyavāyabodhakatvāt..). In other words, this smṛtivākya is a nindārthavāda.

A nindārthavāda vākya does nindā of the niṣedhya (here Vedaśravaṇa, etc. by Śūdras), and thus points to niṣedhavākya in Vedādiśāstras. Medhātithi (in his Manubhāṣya on Manusmṛti 2.241) also explains that from such a severe daṇḍa (stated by Gautama), one should infer the nindya (or niṣedhya) is a severe pāpakarman. And such ninditakarman (niṣiddhakarman) performed by a Śūdra, leads to his patana (yato dhāraṇe śarīrabhedastasyāmnātaḥ / tato daṇḍamahattvāt mahadetadakāryamanumīyate / ninditakarmābhyāse patanaṁ).

Therefore, it should be clear that smṛtikāra Gautama is stating not a daṇḍa in his dharmasūtra (2.3.4) for a Śūdra, but instead a nindārthavāda. If there was such a daṇḍa in real enjoined by śiṣṭas (and possibly by some pralīnaśākhā of Veda), it doesn't make any sense why it seems to have no mention at all in nītiśāstras (especially those of Rājanīti).
Instead, this smṛtivākya is usually quoted by most ācāryas (Śaṅkara, etc.) when discussing anadhikāra of Śūdras in Vedaśravaṇa, etc., emphasizing on the niṣiddhakarman being varjita.

Now, is Gautama's vacana here stating a prāyaścitta for Śūdra, who does Vedaśravaṇa, etc. ? As per some ācāryas, Gautama states a prāṇāntika prāyaścitta here, not a daṇḍa.
Both Ānandagiri & Rāghavānanda consider it to be prāyaścitta and not daṇḍa.

vedamupaśṛṇvataḥ trapujatubhyāṁ karṇapūraṇamiti śruteḥ prāṇāntikaprāyaścittaśravaṇāditibhāvaḥ /
~ Rāghavānanda's bhāṣya on Manusmṛti (1.91)

paṭhyamānaṁ vedaṁ samīpe pramādādeva śṛṇvataḥ śūdrasya pratyavāyaprāyaścittālocanāyāṁ sīsalākṣabhyāṁ santaptabhyāmatidrutābhyāṁ śrotradvayapūraṇaṁ kāryamityarthaḥ /
~ Ānandagiri's Nyāyanirṇaya ṭīkā on Śāṅkarabhāṣya on Brahmasūtra (1.3.38)