Yes, a lay person can baptize in the case of emergency.
From the *Catechism of the Catholic Church:
*1256 The ordinary ministers of Baptism are the bishop and priest and, in the Latin Church, also the deacon.57 In case of necessity, anyone, even a non-baptized person, with the required intention, can baptize58 , by using the Trinitarian baptismal formula. The intention required is to will to do what the Church does when she baptizes. The Church finds the reason for this possibility in the universal saving will of God and the necessity of Baptism for salvation.59
1284 In case of necessity, any person can baptize provided that he have the intention of doing that which the Church does and provided that he pours water on the candidate’s head while saying: “I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.”