Drawn to a stranger, a girdle-breaker,
was a greycloak born in the year of trees
defied the powers while still standing tall
yet entrapped by the sweetest power of all.
Luthien
Lúthien Tinúviel was the only daughter of King Thingol of Doriath and Melian the Maia.
Luthien: (this one I think more likely): "Drawn to a stranger a girdle breaker": If "girdle breaker" is meant to describe the "stranger" (which seems the most natural reading to me) then the stranger is Beren; and Luthien, then, is the one drawn to the stranger. This also makes sense in that Beren was a stranger in Doriath, not Luthien. Luthien was only a stranger to Beren himself. "Was a gray cloak": Thingol was "Gray cloak" (as pointed out above); saying A gray cloak suggests a member of his House or family; it can also be taken as a double-meaning referring to the shadowy cloak Luthien wove from her hair. "Born in the year of trees": THE year is something of a problem, I don't know what that means, but Luthien was born in Middle-earth at the time the Two Trees were alive in Valinor. "Defied the powers..." Note the plural. Beren defied Morgoth, but Luthien defied both Morgoth and, later Mandos (it is possible to dispute that her attitude toward Mandos was actually defiant-- more pleading or persuasive, perhaps-- but I think my interpretation will do for the purpose of the riddle at least). Thus Luthien defied more than one power. And of course the last line applies.
Tolkien Gateway: Lúthien