Mammary gland development and lactation
There is a comprehensive 2012 review of the development of the mammary gland by Macias and Hinck which covers the poster’s question(s). I shall try to summarize the points they make regarding the development of alveoli and their role in milk secretion, ‘borrowing’ two of their illustrations to do so.
Development of mammary gland and role of hormones


At birth there is a rudimentary system consisting of a few rudimentary ductal system.

Until puberty this system grows along with the rest of the organism, under the same hormonal influences that affect other tissues.

At puberty oestrogen — in concert with growth hormone and insulin-like growth factor — accelerates the growth of this ductal system, and its branching is subsequently stimulated by progesterone.

It is only in pregnancy that alveoli form, with a continued requirement for progesterone (perhaps partially indirect) and a specific requirement for a prolactin — which is secreted both from pituitary and — as a different molecule, placental lactogen — from the placenta. The alveoli express the genes for the synthesis of specific milk proteins such as casein, α-lactalbumin and β-lactoglobulin.



[Lactating Mammary Gland: Alveolar cells shown in pink (nuclei blue and milk droplets white) with surrounding adipose tissue yellow]
Oxytocin does not affect the development of the mammary gland (as is made clear in the reference cited by the poster). After parturition it is released from the pituitary in response to the nervous stimulus of suckling and causes the myoepithelial cells around the alveoli to contract causing ejection of the milk.
It should be mentioned that the alveolar cells apoptose on weaning, being replaced by adipocytes. However new alveolar can develop from undifferentiated epithelial cells during a subsequent pregnancy.
Regarding the poster’s specific questions
Q1 The article doesn’t mention anything about development of mammary alveoli, though. How does that happen, then?
A1 The development of the mammary alveoli occurs during pregnancy, under the influence of prolactin/placental lactogen and progesterone.
Q2 I know milk formation primary requires prolactin, oxytocin and indirectly, oestrogen.(4) So does this process wait till pregnancy?(If yes, then the lobes and branches are devoid of any lumen, and they remain empty until pregnancy, which seems skeptical to me.)
A2 The poster’s statements are not completely accurate. Milk formation does not require oestrogen, and oxytocin only affects it in so far as failure to remove milk causes involution. The ducts are indeed devoid of the alveolar lumen until pregnancy, and return to this state on weaning. It is not clear why you are sceptical that this is so. The mammary gland development after puberty prepares the ductal network, but alveolar cells only arise when they are required. Pregnancy is quite long enough for them to develop.
Q3 Can lactation occur without alveoli formation?
A3 I would think not, although the situation regarding neonatal milk secretion (witch’s milk) is unclear because of the obvious ethical barriers to its study in humans. The increase in breast nodule size is suggestive of development. So my opinion is primarily based on argument. The formation of milk requires cells with a specific pattern of gene expression, i.e. of milk proteins and metabolic enzymes that are required for fat formation. It also needs a structure and organization that allows the milk to be secreted into a duct. That is what an alveolus is. Therefore I would imagine that in these circumstances the rudimentary mammary ducts of a new-born infant develop alveoli under maternal hormonal influence.
Postscript
This is a topic I worked on for my doctorate, but have not had contact with for many, many years. It was interesting reading the review — how the technology has changed! I also find it curious that the review makes no mention of corticosterone, as one of the earliest systems for observing alveolar development in vitro was in explants of mammary gland from pregnant mice cultured in defined medium with insulin, prolactin and corticosterone. Perhaps the corticosterone was mimicking what is now known to be the effect of progesterone in vivo.