Sources on the lifespan of Dhamma

This topic is the reason that why saṅgha at 1st saṅgayanā arrange tipitaka content like that. Because they realize to keep lifespan of buddhism. See ruben2020's answer above. For pali source. In my opinion, I think this is sāriputta-aggasāvaka's teaching because he authored saṅgītisutta, and abhidhamma. Also this comment appear in ānanda's, and sāriputta's commentary, too.

Vinaya pitaka, cuḷavagga, bhikkhunikhandhaka:

‘‘sace kho tvaṃ, gotami, ime aṭṭha garudhamme paṭiggaṇheyyāsi, sāva te bhavissati upasampadā’’tiฯ

‘‘seyyathāpi, bhante ānanda, itthī vā puriso vā daharo, yuvā, maṇḍanakajātiko sīsaṃnahāto uppalamālaṃ vā vassikamālaṃ vā atimuttakamālaṃ [adhimattakamālaṃ (syā.)] vā labhitvā ubhohi hatthehi paṭiggahetvā uttamaṅge sirasmiṃ patiṭṭhāpeyya; evameva kho ahaṃ, bhante, ānanda ime aṭṭha garudhamme paṭiggaṇhāmi yāvajīvaṃ anatikkamanīye’’tiฯ

atha kho āyasmā ānando yena bhagavā tenupasaṅkami, upasaṅkamitvā bhagavantaṃ abhivādetvā ekamantaṃ nisīdiฯ ekamantaṃ nisinno kho āyasmā ānando bhagavantaṃ etadavoca – ‘‘paṭiggahitā, bhante, mahāpajāpatiyā gotamiyā aṭṭha garudhammā, upasampannā bhagavato mātucchā’’tiฯ

‘‘sace, ānanda, nālabhissa mātugāmo tathāgatappavedite dhammavinaye agārasmā anagāriyaṃ pabbajjaṃ, ciraṭṭhitikaṃ, ānanda, brahmacariyaṃ abhavissa, vassasahassaṃ saddhammo tiṭṭheyyaฯ yato ca kho, ānanda, mātugāmo tathāgatappavedite dhammavinaye agārasmā anagāriyaṃ pabbajito, na dāni, ānanda, brahmacariyaṃ ciraṭṭhitikaṃ bhavissatiฯ pañceva dāni, ānanda, vassasatāni saddhammo ṭhassatiฯ

‘‘seyyathāpi, ānanda, yāni kānici kulāni bahutthikāni [bahuitthikāni (sī. syā.)] appapurisakāni, tāni suppadhaṃsiyāni honti corehi kumbhathenakehi; evameva kho, ānanda, yasmiṃ dhammavinaye labhati mātugāmo agārasmā anagāriyaṃ pabbajjaṃ, na taṃ brahmacariyaṃ ciraṭṭhitikaṃ hotiฯ

‘‘seyyathāpi , ānanda, sampanne sālikkhette setaṭṭikā nāma rogajāti nipatati, evaṃ taṃ sālikkhettaṃ na ciraṭṭhitikaṃ hoti; evameva kho, ānanda, yasmiṃ dhammavinaye labhati mātugāmo agārasmā anagāriyaṃ pabbajjaṃ, na taṃ brahmacariyaṃ ciraṭṭhitikaṃ hotiฯ

‘‘seyyathāpi, ānanda, sampanne ucchukkhette mañjiṭṭhikā [mañjeṭṭhikā (sī. syā.)] nāma rogajāti nipatati, evaṃ taṃ ucchukkhettaṃ na ciraṭṭhitikaṃ hoti; evameva kho, ānanda, yasmiṃ dhammavinaye labhati mātugāmo agārasmā anagāriyaṃ pabbajjaṃ, na taṃ brahmacariyaṃ ciraṭṭhitikaṃ hotiฯ

‘‘seyyathāpi, ānanda, puriso mahato taḷākassa paṭikacceva āḷiṃ bandheyya yāvadeva udakassa anatikkamanāya; evameva kho, ānanda, mayā paṭikacceva bhikkhunīnaṃ aṭṭha garudhammā paññattā yāvajīvaṃ anatikkamanīyā’’tiฯ

But upāli-etadagga commented, at 1st saṅgāyanā, about above context:

[403] kumbhathenakehīti kumbhe dīpaṃ jāletvā tena ālokena paraghare bhaṇḍaṃ vicinitvā thenakacorehiฯ

setaṭṭhikā nāma rogajātīti eko pāṇako nāḷimajjhagataṃ kaṇḍaṃ vijjhati, yena viddhattā nikkhantampi sālisīsaṃ khīraṃ gahetuṃ na sakkotiฯ

mañjiṭṭhikā nāma rogajātīti ucchūnaṃ antorattabhāvoฯ mahato taḷākassa paṭikacceva āḷinti iminā pana etamatthaṃ dasseti – yathā mahato taḷākassa āḷiyā abaddhāyapi kiñci udakaṃ tiṭṭheyya, paṭhamameva baddhāya pana yaṃ abaddhapaccayā na tiṭṭheyya, tampi tiṭṭheyya; evameva ye ime anuppanne vatthusmiṃ paṭikacceva avītikkamanatthāya garudhammā paññattāฯ tesu apaññattesupi mātugāmassa pabbajitattā pañceva vassasatāni saddhammo tiṭṭheyyaฯ paṭikacceva paññattattā pana aparānipi pañcavassasatāni ṭhassatīti evaṃ paṭhamaṃ vuttaṃ vassasahassameva ṭhassatītiฯ vassasahassanti cetaṃ paṭisambhidāpabhedappattakhīṇāsavavaseneva vuttaṃฯ tato pana uttarimpi sukkhavipassakakhīṇāsavavasena vassasahassaṃ, anāgāmivasena vassasahassaṃ, sakadāgāmivasena vassasahassaṃ, sotāpannavasena vassasahassanti evaṃ pañcavassasahassāni paṭivedhasaddhammo ṭhassatiฯ pariyattidhammopi tāniyevaฯ

Please see the essay "The Coming Buddha, Ariya Metteyya" by Ven. Sayagyi U Chit Tin:

During the period from the time of Buddha Gotama to the minimum life span, the Buddha's Dispensation (Buddha-sasana) will disappear. When the Buddha agreed to create the Bhikkhuni Sangha, he told Ven. Ananda that the Sasana would last only half as long because of this. Instead of lasting one thousand years, it would last five hundred years. The commentary on the Abhidhamma text, Dhammasangani, says that when the First Buddhist Council convened by Ven. Maha-Kassapa rehearsed the Pali Canon, this made it possible for the Sasana to endure for five thousand years.[48]

The commentaries on the Vinaya Pitaka[49] and the Anguttara-nikaya[50] say that the eight important rules which the Buddha gave to the Bhikkhuni Sangha will make his Teachings last for five thousand years rather than five hundred. There will be one thousand years for Arahats who attain analytical insight, one thousand years for Arahats without those attainments, one thousand years for Non-returners, one thousand years for Once-returners, and one thousand years for Stream-winners. After these five thousand years of penetration of the true Doctrine (pativedha-sadhamma),[51] the accomplishment in the texts (pariyatti-dhamma) will remain. After the accomplishment in the texts disappears, the signs (linga) will continue for a long time.

In the commentary to the Theragatha[52] the Sasana is said to consist of five periods: (1) the age of deliverance (vimutti-yuga), (2) the age of concentration (samadhi-yuga), (3) the age of morality (sila-yuga), (4) the age of learning [the texts] (suta-yuga), and (5) the age of generosity (dana-yuga). Ven. Dhammapala says, concerning the disappearance of learning, "In a region where there is no purity of morality, accomplishment (in the texts) remains through taking up great learning, through the desire to acquire, etc. But when accomplishment in the summary [i.e., the Patimokkha] is completely ended, it disappears. From that time on, only the mere sign (linga) remains. Then, having accumulated riches in various ways, they give away gifts (dana); this, truly, is the last right practice. Then, [the period starting] after the disappearance of learning is the last time (pacchima-kala). Others say that it is from the time of the disappearance of morality." According to the tradition in Burma, the Sasana will last five thousand years. The five periods will occur twice. The first half of the Sasana has just passed, with each of the five periods lasting five hundred years. We are now in the second half, when these periods will be repeated, each lasting for another five hundred years.

Footnotes:

[48] As 27, see Expos. 35.
[49] Sp 1291.
[50] Mp IV 136f.

List of Abbreviations:

As =   Atthasalini (trans., Expos.).
       BN 630/862 = Bibliotheque nationale, Pali mss 
       630 and 862, commentary on Anag. We thank Mme J. 
       Filliozat for making available a copy of her 
       transcription of this text.
Expos.=The Expositor (As).
Sp =   Samantapasadika (commentary on the Vinaya Pitaka).
Mp =   Manorathapurani (commentary on the Anguttara Nikaya).