Are monasteries catholic? What if I was baptized Lutheran and want to be in a monastery?

There are monasteries that aren't Catholic...also, many religious communities also have groups of lay people who wish to live a similar lifestyle without being actual members

However, to be an actual monk or nun living in a Roman Catholic religious community like St. Meinrad or the Sisters of St. Benedict in Ferdinand, you would first have to become Catholic, and speaking to a priest would be an excellent idea.

You would need to come home to the Catholic Church. I recommend speaking to a priest.