The sacrifice of Christ redeems first himself, and then us. In his role as redeemer, and the first to effect the redemption, he may rightly be name "firstfruits" unto God, for Christ is the first fruit of the eternal plan that created this earth with the purpose to perfect mankind. As the one who made redemption possible, our redemption comes through him.
Lehi uses the word "intercession" which might be confused with the concept of saintly intercession in Catholic theology. There is a difference in concept, even though the same word is used. Christ intercedes for us because he is the one who has established the gate through which we may be reconciled with God. There is no other way for this to be done, and therefore our redemption is the result of his intercession. Our redemption is not the result of Christ's pleas for us. His actions were plea sufficient, and the rest of the journey is ours to make. Note that Lehi underscores our responsibility in this process when he indicates that salvation is only for "they that believe in him."