Can a cyst on the spleen cause left abdominal pain?

Maybe: It is unlikely but would depend on the size. Most cysts in spleen are small and do not cause pain. Very large cysts can, however, cause pain.

Yes: Splenic cysts if large will irritate the diaphragm and cause left uppper quadrant pain. Most cysts are benign, some are infectious or parasitic and less frequent traumatic. A ct scan should be diagnostic. Benign cysts can be aspirated laparoscopically. If malignancy splenectomy might be necessary.