In what way is "Tithonus" a dramatic monologue in an elegiac strain?

Tennyson's poem "Tithonus" is generally considered a dramatic monologue as it fits within the standard definition of the genre. A dramatic monologue is a poem spoken by a first person narrator with an indefinite addressee, very much like a soliloquy in a drama. Often, the dramatic monologue, as well as voicing the specific issues or concerns of the narrator, acts as a psychological portrait of the narrator. Tithonus is written in the first person voice of a character from ancient Greek myth. He was a mortal lover of Eos, the goddess of the dawn, who asked that Zeus grant him immortal life but for got to ask for eternal youth. The poem is a lament spoken in his voice.

Although it is not an elegy in the sense of being a poem specifically memorializing the death of a person, it is a mournful poem concerned with themes of mortality and inspired by the death of Tennyson's friend Hallam.