A poem written on the death of someone loved and lost

One word substitute is Elegy.

Ode: a lyric poem, typically one in the form of an address to a particular subject, written in varied or irregular metre.
Epic: a long poem, typically one derived from ancient oral tradition, narrating the deeds and adventures of heroic or legendary figures or the past history of a nation.
Sonnet: a poem of fourteen lines using any of a number of formal rhyme schemes, in English typically having ten syllables per line.
Elegy: (in modern literature) a poem of serious reflection, typically a lament for the dead.