Can lay people baptize?

Well, technically yes; but only in an emergency situation. A reading of the Code of Canon Law, Section 849-878 (available in Vatican site) will give a detailed idea of practical steps to be followed in administering the sacrament of baptism, both in ordinary and extraordinary circumstances. 

To summarise it, in an emergency situation, when there is an imminent danger of death due to illness or external threat, and there is no time to get a priest to administer baptism, anyone (including a non-christian) can administer a valid baptism provided the baptiser has the intention to do what the Church requires, uses the correct formula of words (In the name of the Father, Son and Holy Spirit) and performs the correct action of pouring water over the person. 

In normal circumstances, the minister of baptism should be a bishop or a priest. Deacons also can minister in the Latin Rite. Baptism is ordinarily the responsibility of the parish priest, should take place only in a church, and that too the parish church of the child’s parents.