In classical mythology, the deer or stag was associated with the ancient Greek goddess, Artemis (or her Roman counterpart, Diana), in her role as the virginal huntress. One popular myth tells the story of the hero Actaeon, who, after witnessing the goddess bathing, was turned into a stag. He was chased by his own hunting hounds and perished.
Such a lamp could have been given as an offering to Artemis, or belonged to a young hunter, thereby evoking the goddess’s protection and guidance.
For more information about the meanings of animals in Roman art, see our relevant blog post: Animal Symbolism in Roman Art.