why do the three lesser lights have those specific positions

The three lesser lights are situated in the East, South, and West 1. This placement follows the daily course of the sun, which rises in the east, reaches its meridian in the south, and sets in the west 1. No light is placed in the North because the sun is then below the horizon and casts no rays from that quarter 1.

These positions also align with the governance of the lodge and its principal officers. Mackey explains that the three lights represent the Sun, the Moon, and the Worshipful Master 2. Under this symbolic scheme, the officers who exercise authority correspond to the sun in its three manifestations: the Master in the East represents the rising sun, the Junior Warden in the South represents the meridian sun, and the Senior Warden in the West represents the setting sun 2.

The three greater lights are the Holy Scriptures, the Square, and the Compasses, displayed in intimate conjunction with the Square and Compasses resting upon the open Sacred Volume as their foundation 3. Revealed to the candidate through the agency of the three lesser lights, they form the central emblem upon which his attention is directed upon receiving light 3.

Claudy presents the Great Lights as the rule and guide for faith and practice, alongside the tools dedicated respectively to the Craft and to the Master 4. In general Masonic symbolism, Mackey observes that the combined Square and Compasses denote a Mason's duty to the Fraternity and to himself, serving as the badge and token of brotherhood 2.

Wilmshurst provides a mystical reading of the triad, interpreting the three lights as a blueprint of human nature and its divine origin 3. In his view, the Sacred Volume represents the unwritten Eternal Word or Divine Wisdom that forms the base of human existence 3. The Square resting upon it signifies the human soul as originally created in a state of perfection 3. The Compasses symbolize the Spirit, representing the active functional energy and spiritual vitality of that soul 3. Placed together in conjunction, the three greater lights confront the candidate with the ultimate source and spiritual possibilities of his own being 3.