D&C 107:16 is part doctrine, part prophesy.
The administration of the Aaronic Priesthood doesn't operate by lineage now, but it will one day.
Although the Aaronic Priesthood is conferred in the Church today without restriction to the lineage of Aaron, the keys of this priesthood rightly belong to the firstborn of the seed of Aaron, and in the restoration of all things the office of bishop (president of the priests) will once again be conferred on one of that lineage, as it is designated by revelation to the president of the Church (D&C 84:14–21; 107:13–17).
Bible Dictionary, Aaronic Priesthood
This is part of the more general "Restoration of the Gospel", following the apostasy of the Original Church.
And he shall send Jesus Christ, which before was preached unto you:
Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
Acts 3:20-21 (emphasis added)
While this restitution/restoration is often ascribed to events in the 1830s -- like the formation of the LDS Church -- it actually began long before then, and is not yet over.