Let's first understand What a Shiva Lingam is.:
Significance of a Shiva-Lingam.:
According to Skambha (Cosmic Pillar/Agni Lingam) Shuktam of Atharva Veda.:
“hiraṇyagarbhám paramám anatyudyáṃ jánā viduḥ |
skambhás tád ágre prā́siñcad dhíraṇyaṃ loké antarā́ |” (Atharva Veda 10:7:28).
“Men know Hiranyagarbha as supreme and inexpressible: In the beginning, in the midst of the world, Skambha poured (gave birth to) that gold (universe)".
“yásmin bhū́mir antárikṣaṃ dyáur yásminn ádhy ā́hitā |
yátrāgníś candrámāḥ sū́ryo vā́tas tiṣṭhanty ā́rpitāḥ skambháṃ táṃ brūhi katamáḥ svid evá sáḥ |” (Atharva Veda 10:7:12).
“Who out of many, tell me, is that Skambha On whom as their foundation earth and firmament and sky are set; In whom as their appointed place rest Fire and Moon and Sun and Wind?”
So, Skhambha (Linga) contains all worlds within it since it contains Hiranyagarbha but Skhambha extends beyond the Hiranyagarbha also because Hiranyagarbha is just a portion fo the Skhambha.
“yát paramám avamám yác ca madhyamáṃ prajā́patiḥ sasr̥jé viśvárūpam |
kíyatā skambháḥ prá viveśa tátra yán ná prā́viśat kíyat tád babhūva |” (Atharva Veda 10:7:8).
“That universe which Prajāpati created, wearing all forms, the highest, midmost, lowest, How far did Skambha penetrate within it? What portion did he leave unpenetrated?”
“br̥hánto nā́ma té devā́ yé 'sataḥ pári jajñiré |
ékaṃ tád áṅgaṃ skambhásyā́sad āhuḥ paró jánāḥ |” (Atharva Veda 10:7:25).
“Great, verily, are those Gods who sprang from non-existence into life. Further, men say that that one part of Skambha is nonentity”.
So, Skambha Represents Linga/Purusha and Hiranyagarbha represents the known Universe or Brahmāmda/Prakritik Womb or Prakriti/Pitha/Yoni.
Skanda Purana calls Mata Tripura Sundari as “brahmanda garbhini” in 774th name, which means “She who keeps the universe in her womb”.
Same is depicted in below verses from Sri Vishnu Purana.:
"purushAdHishtHitatvAshcha pradhAnAnugrahENa cha | mahadAdyA vishEshAntA hyAndamutpAdayanti te | tatkramENa vivrudhhaM sajjalabudbudavatsamam | bhUtEbhyONdam mahAbuddhE mahatdudakEshayaM | prAkrutam brahmarUpasya vishNoh sthAnamanuttamam | tatrAvyaktaswarUpOsou vyaktarUpO jagatpatih | vishNubrahmaswarUpENa swayamEva vyavastitah | mErurulbamabhUtasya jarAyushcha mahIdharAh | garbhOdakam samudrAshcha tasyAsansumahAtmanah | sAdridweepasamudrAscha sajyOtirlOkasangrahah | tasminnaNdEbhavidvipra sadEvAsuramAnushah |" (Vishnu Purana 1:2:44-48).
“With the assistance of prakriti, from mahat to vishesha all these elements of prakriti when pervaded by purusha it formed a universal egg (brahmanda). O you of great intelligence listen! Then it started increasing its size like a water bubble and became a huge oval-shaped entity. This which is called as Hiranyagarbha (golden womb) is an awesome form of Vishnu. Inside that golden womb (hiranyagarbha), that unmanifest lord of the universe viz. Vishnu manifested himself as Brahma. That Hiranyagarbha [which is the golden womb] consisted of Sumeru and other mountains were the jarayu (the skin which covers the embryo), and the oceans were the fluids of the womb. O learned sage Maitreya! within that womb (hiranyagarbha) all the mountains, all the islands, planets, all celestial abodes, all deities, all demons, humans and all other cratures got manifested".
“Kesava (Krishna) is that devoted worshipper of Rudra who has sprung from Rudra himself. Kesava always worships the Lord Siva, regarding his Linga emblem to be the origin of the universe. The God having the bull for his mark cherisheth greater regard for Kesava”. (MBH 7:172:89-90).
Rudra Hridayo Upanishad (1:20).:
“rudro li~Ngamumaa piiTha.n tasmai tasyai namo namaH |”,
“Rudra is Linga. Uma is Pitha, prostrations to Him and Her”.
Significance of Milk in Scriptures.:
Atharva Veda glorifies cow as follows. Cow is heaven and earth and she is Vishnu. In below verses note that the sAdhyas (enlightened spirits) who have drunk her milk, pay adorations to her milk, note that here MILK is called SOMA. Note another point that the merit of giving a cow to that high-souled person who understands the real meaning of these verses, goes to the third region of the sky (viz. Sahasrara).
“vaśā́ dyáur vaśā́ pr̥thivī́ vaśā́ víṣṇuḥ prajā́patiḥ | vaśā́yā dugdhám apibant sādhyā́ vásavaś ca ye | vaśā́yā dugdháṃ pītvā́ sādhyā́ vásavaś ca ye | té vái bradhnásya viṣṭápi páyo asyā úpāsate | sómam enām éke duhre ghr̥tám éka úpāsate | yá eváṃ vidúṣe vaśā́ṃ dadús te gatā́s tridiváṃ diváḥ |” (Atharva Veda X:10:30-32).
“The Cow is Heaven, the Cow is Earth, the Cow is Vishnu, Lord of Life. The Sādhyas and the Vasus have drunk the out-pourings of the Cow. When these, Sādhyas and Vasus, have drunk the out-pourings of the Cow, They in the Bright One's dwelling-place pay adoration to her milk. For Soma some have milked her: some worship the fatness she hath poured. They who have given a cow to him who hath this knowledge have gone up to the THIRD region of the sky”.
Aditi (Uma), is the cow who downpours her milk.
Satapatha Brahmana (14:2:1:7).:
“the cow is Aditi”.
Also, Rig Veda supports it as follows.:
“pīpāya dhenuraditirṛtāya janāya mitrāvaruṇā havirde |“ (Rig Veda 1:153:3).
“O Mitra-Varuṇa, Aditi the Milch-cow streams (milk) for the rite, for folk who bring oblation”,
Aditi is the earth, heaven and atmosphere.
“aditirdyauraditirantarikṣam|” (Rig Veda 1:89:10).
“Aditi is the heaven, Aditi is mid-air”.
“aditir asyAm eva pratisHThAyAnu paHyati |” (Yajur Veda VI:1:5:3).
“Aditi indeed is this earth; verily taking his stand on it he sees”.
Comparing these Vedic verses with the aforementioned verse on cow we know that Aditi (Uma) is the heaven & earth and it is she who is the cow whose MILK is SOMA and she is also ‘Vishnu’ as I have already mentioned in this answer of mine.
This has been clearly stated in Adi Shankara’s Soundarya Lahari hymn as follows.:
“Twa stanyam manye dharanidhara kanye hridhayatha |
Paya paraabhaara parivahathi saaraswathamiva |
Dhayavathya dhattham dravida sisu raaswadhya thava yat |
Kaveenam proudana majani kamaniya kavayitha |” (Soundarya Lahari, stanza 75).
“Oh daughter of the king of mountains, I feel in my mind,That the milk that flows from your breast, Is really the goddess of learning, Sarswathi,In the form of a tidal wave of nectar.For , milk given by you ,who is full of mercy,Made the child of Dravida, The king among those great poets,Whose works stole one’s mind”.
So, milk here is Soma. Soma is generally considered as some intoxicating drink but it is not any ordinary milk, it is in fact the milk of ‘Brahma jnanam (Brahman knowledge)’. Which gives one Moksha.
Therefore, Uma/Vishnu gives knowledge of Brahman (Brahma Jnanam) to yogis.
स तस्मिन् एव आकाशे स्त्रियम् आजगाम बहुशोभमानाम् उमाम् हैमवतीम् ताम् ह उवाच किम् एतत् यक्षम् इति ॥१२॥
3.12. In that space itself (where the Yaksha had disappeared) Indra approached an exceedingly charming woman. To that Uma decked in gold (or to the daughter of the Himalayas), he said: "Who is this Yaksha?"
सा ब्रह्म इति ह उवाच । बृह्मणो वा एतत् विजये महीयध्वम् इति, ततो ह एव विदाञ्चकार बृह्म इति ॥१॥
4.1. She said: "It was Brahman. In the victory that was Brahman's you were reveling in joy". Then alone did Indra know for certain that It was Brahman.
ओङ्कारं रथमारुह्य विष्णुं कृत्वाथ सारथिम् । ब्रह्मलोकपदान्वेषी रुद्राराधनतत्परः॥ तावद्रथेन गन्तव्यं यावद्रथपथि स्थितः । स्थित्वा रथपथस्थानं रथमुत्सृज्य गच्छति॥२-३॥
Mounted on the chariot in the form of Omkara and making Lord Vishnu as his charioteer (guru), the wise man, thinking of the supreme position of Brahmaloka (City of Brahman), one should always remain engrossed in the worship of Lord Rudra, the God of gods and should go by that chariot in the form of Pranava until the path that can be traversed by the chariot is completed. When that path (goal) is completed, then leaving that chariot man automatically reaches the place of the owner of the chariot (Brahman). ॥ 2-3॥
Conclusion.: So yes, Milk is Soma/Amrita which gives the knowledge of Brahman and Nourishment to the Universe which is in the form of Shiva-Lingam.
।। ॐ तत् सत् ।।