John Gill Commentary Leviticus 14:19

"And the priest shall offer the sin-offering, and make atonement for him that is to be cleansed because of his uncleanness: and afterward he shall kill the burnt-offering;" — Leviticus 14:19 (ASV)

And the priest shall offer the sin offering This was the ewe lamb, according to the rite of every sin offering, as Aben Ezra says; and was typical of Christ, as all such offerings were, who was made sin and a sin offering for his people: and make an atonement for him that was to be cleansed from his uncleanness; for it seems the atonement was not perfected by the trespass offering and all the preceding rites; but a sin offering was necessary both on account of moral uncleanness, the cause of the leprosy, and of ceremonial uncleanness by it: and afterward he shall kill the burnt offering; the other he lamb; the burnt offering for the most part following the sin or trespass offering as a gift by way of thankfulness, atonement being made for sin by the other offerings; which also was typical of Christ, as all burnt offerings were.