Lehi partook of the fruit of the tree. Linguistically, what does the word "partake" mean? If you partake, you become a participant, not just a taker of some kind. The word "partake" comes from the Latin particeps, meaning "participant," and thus has a stronger meaning than just eating or taking a piece or a part of something. When you partake of something—as when you partake of the sacrament—you become a participant. It becomes part of you, and you become part of it yourself.
Mark D. Ogletree, "’That My Family Should Partake’," Religious Educator 17, no. 1 (2016).
"Remember Lehi’s encounter with the tree of life? As soon as he partook of the fruit, his deepest desire was that his ‘family should partake of it also’ (1 Nephi 8:12). Lehi’s desire wasn’t to share his initial joy with neighbors or friends, or even fellow Saints. Foremost on his mind was his family; his desires were riveted on sharing his gospel knowledge with those he loved the most." (p. 95)