Li Dan's dragon-and-phoenix match
Li Dan is the future Emperor Ruizong of the Tang, and the episode behind the lot is the one in which his marriage is arranged across a gap in station, the "dragon and phoenix" pairing of the title. Lot books attach it here because the story is about a match that looked improbable from the outside and held.
The fourth line uses an image from the Book of Songs. Dreaming of a bear was the classical omen of a son, dreaming of a snake the omen of a daughter, so "the bear enters the dream" carried a specific meaning to a reader four hundred years ago. We keep it on the page because it is in the source text, and we do not treat it as a prediction about anyone's children.
Traditional palace assignment: Chen palace (宮位), one of the twelve branch positions the old lot books use to file each verse.
Reading lot 21
The first two lines say that pairing is not accidental. Read at face value that is a statement about fate, and it is worth being plain about the limit: a four-line verse cannot tell you whether a particular person is willing, and nothing here reports the other party's intentions.
What the lot is more useful for is its third line, which makes the good outcome conditional on a meeting. Dragon and snake are two of the twelve branches again, and the line places the resolution at the point where two things come together, never at the point where one of them tries harder. If you drew this about someone you have not spoken to, the verse does not supply their answer. If you drew it about a relationship already in motion, it points at whether the two sides are actually converging on the same plan.
Five characters in this lot differ between the two published traditions, all of them in the last two lines, so the version on your slip may read slightly differently from the version here.
A verse can give you a frame for thinking about a situation. It cannot report what another person has decided, and it cannot confirm that a particular event will happen.