CLC was actually founded by a Belgium Jesuit, Jean Leunis in 1563. At that time there were many lay people attracted by the energy and vitality of the then new order of priests and brothers. But being already committed to their spouses and families they could not follow the Jesuit charism in that particular way. Instead they formed sodalities, known as the Sodalities of Our Lady, groups of lay Christians adapting the Jesuit charism and desiring to live a more integrated life of prayer and service, particularly to those most in need. The Christian Life Communities developed  from the Sodalities of Our Lady after Vatican II. The Society of Jesus (Jesuits) continue to have a close relationship with the CLC.

Link to the Jesuit Province in Malta  

Some information on CLC in Malta