How Are The 3 Lunar Months Counted For ʿIddah?

If the woman was divorced on the 1st of the month, then all agree that she will count her 3 months by the sighting of the crescent (hilāl). Therefore, her ʿiddah can be 90, 89, or 88 days.
If she was divorced on any other day, then there is a difference of opinion regarding how to calculate the 3 lunar months:

Menopause at 30 Years of Age: An Exception

In the chapter on ʿiddah, ʿAllāmah Haṣkafī and ʿAllāmah Shāmī mentioned an exception to the rule of 55 years being the age of menopause. 
If a woman became bāligh by age, i.e., by passing 15 lunar years of her life, and never saw a single ḥayḍ her entire life and she reaches the age of thirty (30), the judgment of being a woman in menopause would be issued for her.

Menopause Rulings

Ḥayḍ terminates when a woman reaches the age of menopause.
Age of “losing hope” for Ḥayḍ and Nifās (i.e., Menopausal Age)

Lunar: 55 years. [Preferred Opinion]
Solar: 53 years 4 months.
Rule 1: When a woman reaches the age of 55 and her bleeding stops, the judgement of her being in menopause is passed.
Rule 2: The ʿiddah (for a divorce) of a woman who reaches the age of 55 and is no longer seeing blood is counted as 3 lunar months.

Definitions: Part 1- The Definition of Ḥayḍ [Menstruation]

The Definition of Ḥayḍ
Literal Definition:  To flow.
Sharʿī Definition:
It is a state of ritual impurity. Ḥayḍ is a legal obstacle which prevents a woman from fulfilling such acts of worship which require ṭahārah (purity), such as: Ṣalāh, recitation of the Qur’ān, fasting, entering the Majid, sexual Intercourse, etc.

It is a physical impurity. Ḥayḍ is blood which flows from the [woman’s] womb and exits from the farj dākhil (vaginal opening), even if it is legal (ḥukman) blood without childbirth.

The Importance of Mastering the Masā’il of Menstruation

Through the infinite grace and assistance from Allāh Taʿālā alone, He  has granted us the tawfīq to begin this task of sharing important information and masā’il regarding menses (Ḥayḍ), dysfunctional uterine bleeding (Istiḥāḍah) and lochia (Nifās) mainly sourced from “Manhal al Wāridīn”, ʿAllāmah Ibn ʿĀbidīn al-Shāmī’s رحمه الله commentary on Imām Birgivī’s رحمه الله “Dhukhrul Muta’h-hilīn”.
“The validity of many other rulings is based on this such as: ṣalāh, fasting, reading and touching the Qur’ān, iʿtikāf, entering the Masjid, ṭawāf of Ḥajj, puberty, divorce, ʿiddah, permissibility of intercourse, lineage.” [ʿAllāmah Shuranbalālī رحمه الله]