In a word, No. In 1997, the National Conference of Catholic Bishops with the approval of the Congregation for the Divine Worship and the Discipline of the Sacraments issued the following instruction, entitled “Reflections on the Body, Cremation and Catholic Funeral Rites,” which was incorporated into the Order of Christian Funerals: “The cremated remains of a body should be treated with the same respect given to the human body from which they come. This includes the use of a worthy vessel to contain the ashes, the manner in which they are carried, the care and attention to appropriate placement and transport, and the final disposition. The cremated remains should be buried in a grave or entombed in a mausoleum or columbarium. The practice of scattering cremated remains on the sea, from the air, or on the ground, or keeping cremated remains in the home of a relative or friend of the deceased are not the reverent disposition that the Church requires. Whenever possible, appropriate means for recording with dignity the memory of the deceased should be adopted, such as a plaque or stone that records the name of the deceased” (No. 417).
Therefore, regarding the question at hand, the urn containing the ashes may be sunk into the lake, like a burial at sea, but not scattered.