Luthien had to ask for the choice, but she wasn't half-elven. Her descendants were half-elven; and they were GIVEN the choice. Arwen always knew she would have to choose. So did Elladan and Elrohir. Arwen's choice left a spot open on the ship into the West; but notice that Bilbo and (eventually) Sam also went. The letters say that Gandalf probably also had something to do with it, and perhaps Galadriel (if I remember correctly.) See footnote (on page 327) to letter 246.
Some folks think that Shadowfax went West too.
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...down to the water to see the elves dance and sing upon the midsummer's eve.
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