Lilly's third house is a list that looks miscellaneous and is not: brethren, sisters, kindred, neighbours, short journeys, letters and rumours. What holds it together is proximity. The third is the house of everything close at hand and reachable without ceremony, and a sibling is the type case: a person of the same household and the same generation, neither above the native nor below.
Mercury is the general significator, which follows from the same idea. Mercury governs speech, messages, the short errand and the exchange of news, which is what the third house is for. The sign on the third cusp and the planet ruling it supply the particulars: how many, of what temperament, and on what terms.
The same place carries a much older name. In the Greek scheme the third is Thea, the Goddess, paired with the ninth, Theos, the God, and the Moon has its joy there. Those names sit oddly beside brethren and short journeys, and the mismatch is a useful reminder that the twelve places held different content in the Hellenistic system than the medieval catalogue later gave them. It is why some traditional astrologers still read the third as much for the Moon's affairs, the body and the daily round, as for siblings.
A reading that uses both layers has to keep them apart. The Goddess and the brother are not in one house by coincidence; they are two settlements of a single slot, several centuries apart.
Sources Christian AstrologyWilliam Lilly with Hellenistic Astrology: The Study of Fate and FortuneChris Brennan