The Lament for Gandalf isn't in the book, is it? The only verse about Gandalf in the Lothlorien part is the one Frodo made up.
Now as the companions sat or walked together they spoke of Gandalf, and all that each had known and seen of him came clear before their minds. As they were healed of hurt and weariness of body the grief of their loss grew more keen. Often they heard nearby Elvish voices singing, and knew that they were making songs of lamentation for his fall, for they caught his name among the sweet sad words that they could not understand.Mithrandir, Mithrandir sang the Elves, O Pilgrim Grey! For so they loved to call him. But if Legolas was with the Company, he would not interpret the songs for them, saying that he had not the skill, and that for him the grief was still too near, a matter for tears and not yet for song.