When Lehi first saw the Father sitting upon His throne, the description is as follows: “he thought he saw God, sitting upon his throne, surrounded with numberless concourses of angels, in the attitude of singing and praising their God.” (1 Ne. 1: 8.)
After being ministered to by Christ, (1 Ne. 1: 11) the description changes as Lehi reacts to his endowment of knowledge from the Lord. The record says: “And after this manner was the language of my father in the praising of his God.” (1 Ne. 1: 15.) God the Father has ceased to be the impersonal “God” of verse 8, and has become Lehi’s God by verse 15.
It is in this sense that God becomes “the God of Abraham, the God of Isaac and the God of Jacob.” (Matt. 22: 32.) God established His covenant with Abraham. Then He renewed and established His covenant again with Isaac. Then He renewed it again with Jacob. He was each of their God, by covenanting with each of them. None relied on a covenant given to their father, or grandfather, but each received directly from God a covenant in their own name.
Lehi also covenanted with God. He also knew the Father as “his God.” If you read what happened between verses 8 and 15, you will see how Christ ministers to a man and brings them into a relationship with the Father.
Compare 1 Ne. 1: 11-14 with Revelation 5: 1-8. In both there is a book, and it is Christ who is able to access the book. In both, a prophet, (Lehi and John) are able to then get access to the information which would be otherwise hidden from the world.
Lehi, as a recipient of the covenant directly from God, joined those who could call God “his God.”
It is the God of Lehi in the same way it is the God of Abraham; and the God of Isaac; and the God of Jacob; and the God of Nephi; and the God of Joseph.
Look at 2 Kings 2: 14 and you will see Elisha acknowledging that Elijah also knew God; and Elisha wanted to likewise come to know Him.
Is He also your God? If not, why will you not have Him to be your God? (1Ne. 17: 40.)