Possibly of Canadian origin, Red River Valley was nonetheless very popular in the US. It was established in Canada by 1896 and may have been composed in the 1870s. It begins "from this valley they say you are going...."
Stephen Foster's Beautiful Dreamer probably dates from 1862.
The Star Spangled Banner begins "o say, can you see...?"
Another answer notes Schubert's Doppelgänger, which sets an untitled poem by Heine. There is also Du bist wie eine Blume, by the same poet, writing in the early 19th century.
Schubert also set both of Goethe's poems with the title Wandrers Nachtlied, written in 1776 and 1780. Both are in the second person, though the first may be addressed to the divine and therefore not anonymous.
Going back a bit farther and returning to English, Shakespeare's song "O Mistress mine" from Twelfth Night, 1601 or 1602, has long been a favorite lyric of composers. "... where are you roaming? O, stay and hear your true love's coming..."
As noted in the other answer, this is a literary device that has been in use for centuries, and it should not be difficult to find examples of its use throughout the history of western lyrical poetry.
For a little one-upsmanship with the accepted answer, I note that Sumer is icumin in, dating from around 1260, ends with the line
Wel singes þu cuccu
ne swik þu nauer nu
This means more or less
You sing cuckoo well.
Never stop now.