You've written a sweet tribute to one of the great relationships in The Lord of the Rings. I like the way Legolas looks forward to their last journey. A couple spelling issues caught my eye. In your summary, I think you mean respectively rather than "respectably". In the story, waybread for "laybread" and born for "borne".
Gimli seems as grumpy as ever. Maybe he considers it a weakness to openly display affection toward his friend, considering the history of animosity between Dwarves and Elves. Or maybe, being such a gruff person, he finds it embarrassing to reveal his friendly side.
I found the story very interesting. I hope you're planning to write more on the Fourth Age adventures of these two characters.