It seems spiritual to me.
The pivotal moment doesn't occur when Gimli first sees Galadriel, but when he
begins to see deeper.
"She looke upon Gimli, who sat glowring and sand, and she smiled. And the
Dwarf, hearing the names given in his own ancient tongue, looked up and met her
eyes; and it seemed to him that he looked suddenly into the heart of an enemy
and saw there love and understanding. Wonder came into his face, and then he
smiled in answer."
Love and understanding turn his glower into a smile. When the travelers leave
Lorien, he says he would like a strand of her hair "in memory of your words,"
not of her
face.
(Insert wildly creative footer here.)