Lehi was raised under the tradition of the Law of Moses. There is no reason to think that his sacrifice was anything but an animal sacrifice. The Book of Mormon rarely describes the practice of animal sacrifice. Mosiah 2:3 records, And they also took of the firstlings of their flocks, that they might offer sacrifice and burnt offerings according to the law of Moses. Although little is spoken of this practice, it would have been a consistent part of Nephite worship, especially in the temples that they built. The specific blessing the Lord promised with respect to this practice is found in Ex 20:24, I will come unto thee, and I will bless thee.
Secondly, in Lehi's day, those who offered sacrifice in the temple of Solomon held the Aaronic Priesthood. In order to hold the Aaronic or Levitical priesthood, one had to be a Levite by descent. Lehi was a Manassehite, and therefore would not have held the Levitical priesthood. He must have held the Melchizedek priesthood. However, as with the great prophet Elijah, there is no record of how he received it. Alma suggests that these prophets received the priesthood from the Lord based on their faith, And this is the manner after which they were ordained--being called and prepared from the foundation of the world according to the foreknowledge of God, on account of their exceeding faith and good works; in the first place being left to choose good or evil; therefore they having chosen good, and exercising exceedingly great faith, are called with a holy calling, yea, with that holy calling which was prepared with, and according to, a preparatory redemption for such (Alma 13:3, italics added). Alma also makes it clear that the Melchizedek priesthood was held by the Nephites prior to the coming of Christ, Alma…confined himself wholly to the high priesthood of the holy order of God. (Alma 4:20, see also Alma 13:1-19)