Final answer:
A lyric poem where the speaker addresses someone without their replies being recorded is known as a monologue, which fits the description best out of the given options.
Step-by-step explanation:
A lyric poem in which the speaker addresses someone whose replies are not recorded can be known as a monologue. None of the other options, namely a sonnet, an elegy, or an ode, specifically describe a poem where only one person speaks without recorded replies from another. While an elegy is a sorrowful poem lamenting the dead, an ode is written in praise of its subject, and a sonnet is a 14-line poem with a specific rhyme scheme and structure. The closest option to the description provided in the question is a dramatic monologue, which is a speech from a single person often found in plays, where the speaker's words are recorded but not the replies of any other characters.