Snow-white! Snow-white! O Lady clear!
O Queen beyond the Western Seas!
O Light to us that wander here
Amid the world of woven trees!
Gilthoniel! O Elbereth!
Clear are thy eyes and bright thy breath!
Snow-white! Snow-white! We sing to thee
In a far land beyond the Sea.
O stars that in the Sunless Year
With shining hand by her were sawn,
In windy fields now bright and clear
We see your silver blossom blown!
O Elbereth! Gilthoniel!
We still remember, we who dwell
In this far land beneath the trees,
Thy starlight on the Western Seas.
Then of course there is the hymn of the elves of Rivendell:
A Elbereth Gilthoniel,
silivren penna míriel
o menel aglar elenath!
o galadhremmin ennorath,
Fanuilos, le linnathon
nef aear, sí nef aearon!
In translation (Tolkien's own) this runs:
"O! Elbereth who lit the stars, from glittering crystal slanting falls with light like jewels from heaven on high the glory of the starry host. To lands remote I have looked afar, and now to thee, Fanuilos, bright spirit clothed in ever-white, I here will sing beyond the Sea, beyond the wide and sundering Sea."
I could cite more examples (such as Galadriel's amazing song, which does some very interesting things with the dual pronoun). In all, I counted 10 instances of where her name was invoked as a kind of prayer:
- 7 in The Fellowship of the Ring
- 1 in The Two Towers
- 2 (or arguably, 3) in The Return of the King
What is so interesting about these uses is that they begin to taper off after Lothlorien, as invocations of Varda/Elbereth are replaced by invocations of Galadriel, who the Three Hunters thank in their hearts for the gift of Lembas, and to whom Sam wishfully prays for light and water in Mordor--after which they find both. In fact, whenever the words "the Lady" are used without any other name in The Two Towers and The Return of the King, they always refer to Galadriel.