The organelle in the cell, other than the nucleus, that contains DNA is the mitochondrion.

Mitochondria are double-membraned organelles found in most eukaryotic cells. They are often referred to as the "powerhouses" of the cell because they generate the majority of the cell`s energy in the form of ATP (adenosine triphosphate) through a process called cellular respiration.

Mitochondria have their own circular DNA molecules, known as mitochondrial DNA (mtDNA), which encode some essential proteins and RNA molecules involved in energy production. While the majority of an organism`s DNA is located in the nucleus, mitochondria have their own smaller genome.

Centrioles are cylindrical structures involved in cell division, but they do not contain DNA. The Golgi apparatus is responsible for modifying, sorting, and packaging proteins, but it does not contain DNA. Lysosomes are involved in cellular waste disposal and digestion, but they do not contain DNA either.

Therefore, the correct answer is:

Mitochondrion.