Being a ringbearer, Galadriel's intentions would be bound up with that possession, seems to me. Not only that, her intentions also would have to do with her rulership over Lorien and her care for all Elves and beneficence toward all free peoples. Only Boromir, who brought his own darkness with him into Lorien, saw her as a temptress. The others felt themselves tested rather than tempted. So it seems to me.
Thus, her intentions, I would say, are for the furtherance of the cause of the destruction of the Ring. I think she felt that the Fellowship still had a role to play in helping Frodo get to Mordor, even though she may have had the foresight that it would break. Her intentions therefore seem to me to be to determine how trustworthy to the cause each member of the Fellowship was.
Frodo: hand the Ring to another and give up.
Sam: go back to the Shire.
Pippin: same
Merry: same
Gimli: riches untold
Legolas: to go into the West?
Aragorn: Arwen without the need to prove himself by earning kingship?
Boromir: the Ring, obviously
I'm sure someone could do better than that for speculation.
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