Meneguito is a charming and somewhat rare diminutive of menudo, which can mean 'small' or 'trifling'. In Dominican Spanish, menudo can also refer to a stew or a small, special treat.
In the context of the song, Juan Luis Guerra uses el meneguito de mi fe (the little stew/treat of my faith) to describe how the light of his beloved's gaze nourishes and sustains his faith, much like a comforting meal or a delightful treat. It's a unique and endearing way to express deep affection and spiritual sustenance.
Juan Luis Guerra's "Lámpara Pa' Mis Pies" is a sweet, romantic song about finding true love and how that love becomes your guiding light. It starts with the singer recounting how he went to Boston and met a girl with "ojitos verdes" [green eyes] and immediately fell in love. He gave her everything: his dreams, his coffee maker ("mi greca y mi café"), his guitar, and even a lamp for his feet!
The chorus makes it clear that this "lámpara pa' mis pies" [lamp for my feet] isn't a literal object, but the light of her gaze and the strength of his faith in her. He describes moving into her neck ("me mudé en tu cuello") and taking pictures of her kisses, revealing her laughter. He can't leave home without this metaphorical lamp, which is her love and presence. He even crowns her his queen and gives her songs, showing how completely she illuminates his life.