Can a child baptized Lutheran also be baptized Catholic to attend Catholic church and school?

Baptism in the Lutheran Church is recognized as valid by the Catholic Church :)

If a person is baptized into Jesus the Christ, they don't need another baptism to be a part of God's kingdom.

Since the Catholic Church recognizes the validity of Lutheran baptism, as RickJ says, you should only need to provide a baptismal certificate from the place where the baptism was performed.

If a person is baptized into Jesus the Christ, they don't need another baptism to be a part of God's kingdom.

Quite true, and that baptism does not come with water.

Redtop,
The Lutheran Church and the Catholic Church and others Baptize In the NAME of The Father, Son, and Holy Spirit with water as the bible instructs.
SO the Catholic Church recognizes them as valid.
It is one of the very many ways that many denominations are in agreement with each other.
Peace and kindness,
Fred

Can a child baptized Lutheran also be baptized Catholic to attend Catholic church and school?

No need. Lutheran Baptism is valid in the Catholic Church.

De Maria,
Right you are.
Fred