Leviticus 14:31

Even such as he is able to get, the one for a sin offering, and the other for a burnt offering, with the meat offering: and the priest shall make an atonement for him that is to be cleansed before the Lord.

Cross-reference

In Leviticus 5:7, the same substitution of birds for a lamb is allowed for a guilt offering when the offerer is poor—identical principle.

In Leviticus 15:15, a man with a discharge also offers two birds as sin and burnt offerings—a similar purification ritual.

In Numbers 6:11, the priest offers one bird for a sin offering and one for a burnt offering—identical to the leper's ritual here.

In Numbers 6:10, a Nazirite brings two turtledoves or pigeons to the priest for purification—matching the leper's offering.