Billy Collins' poem is a lyric poem because mainly it expresses highly personal emotions and feelings. Many lyric poems involve musical themes or tones, and in fact in Shakespeare's era the word "lyric" meant that the poem was accompanied by a musical instrument (a lyre). But while Collins' poem doesn't give off a musical idea or theme (unless the sound of a fork scratching across a granite table is music), it does use metaphor and achieves a dramatic impact.

The metaphor has two people, presumably married and in a love partnership who have divorced. (It is known that although un-married couples who have been together for a long time and break up are also involved essentially in a "divorce" of their partnership.) The metaphor of "two spoons" shows two people locked together, snuggling would be a good word, in a warm bed. "Tined" means prongs on a fork -- or...
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