Is there any source which says about the main pupils of Sri Lakulisha and how the sect was propagated in various places of India?
According to Linga Purana, Volume 1, Chapter 24, Translated by J.L.Shastri, there are four disciples having name as: Kusika, Garga, Mitra and Kaurusya. This chapter talks about the twenty eight incarnations of Lord Shiva and it also states that he had four disciples in every incarnation.
124b-133. When the twenty-eighth cycle of four yugas occurs in due order, the glorious son of Parasara named Dvaipayana will become a Vyasa. He is Visnu himself, the grandfather of the worlds. At that time, Vasudeva, black in colour and the best among men and exalted among the Yadus, will be born of Vasudeva. At the same time, by the power of my yogic illusion I the Yogatman will be born as Brahmacarin and inspire awe among the people. On seeing a dead body left in the cremation ground without a claimant, I shall be entering it by the yogic power for the welfare of the brahmins. Along with you and Visnu I will enter the divine and holy cave of the Meru. O Brahma, at that time, I will be known as Lakuli. That holy place where I entered the dead body will be known as Kayavatara—a name that will last as long as the earth lasts. There too the ascetic sons will be born to me. They will be known as Kusika, Garga, Mitra and Kaurusya. They will be great yogic soul and brahmins who will have mastered all the Vedas. They will remain celibate and free from impurities. After attaining the yoga of MaheSvara they will go to Rudra’s world, never to return.