Point of information: Any person above the age of reason can peform a baptism.
Even a person of different faith or even no faith. As long as they intend to do as the Church does. Also in extreme cases a priest that has been laicized can give last rites and hear a final confession. The penetitnt must be in grave danger of death and there must be no other priest to give recourse, but it can legally be done.
Yes, I know all that, and you’re right it’s good to clarify these details. As for baptism, it’s not enough for a person to “intend” to do it as the Church does, it must be performed correctly. For example, look at all the people who have had to get “re-baptized,” or bring back their children, because a trendy priest (ironic that a layperson probably would not take this liberty) said the wrong formula “I baptize thee in the name of the Creator, the Redeemer and the Sanctifier” instead of “Father, Son and Holy Ghost.” Not a valid sacrament.
A laicized priest is not to perform any sacraments, even baptism, except in the cases you mention, which makes sense, so a dying person is not deprived in an emergency. Then he would be allowed to do those sacraments because he is always a priest in the sense Holy Orders cannot be “erased”. That’s why the term is “laicized priest” and the common expression “defrocked” confuses folks.