From the Floating Log at Frogmorton

At Boromir’s hurried funeral Aragorn and Legolas sing their farewell songs to Boromir.  Aragorn sings two, hogging the show.  Gimli says “You left the East Wind to me, but I will say naught of it.”  It’s too bad he didn’t take a shot, though.  If he had, he might have come up with something like this.  (Note that he’s using Shire-reckoning because it scans better):

The Battle of Amon Hen (TTTO The Battle of New Orleans [Johnny Horton])

In 1419 we took a little trip 
Along with the Ringbearer down the mighty Anduin. 
We took a little lembas and I took a lock of hair 
And we met the bloody Uruks at the foot of Amon Hen. 
  
Boromir drew his blade but the Uruks kept a'comin. 
Though there wasn’t quite as many as there was a while ago. He blew his horn and we all came a-runnin' 
But by that time they had the hobbits – where they’re goin’, I don’t know.   
We looked in this glade and we seen poor Boromir. 
There must have been a hundred arrows stickin’ in him here. At first we thought Aragorn was just as dead as he. 
We stood with lowered heads, but then he said to me: 
  
“Boromir drew his blade but the Uruks kept a'comin. Though there wasn’t quite as many as there was a while ago. He blew his horn and we all came a-runnin' 
But by that time they had our friends and where they’re goin’, I might know.”   
Well, Boromir had thought he’d take Frodo by surprise But we all knew what was comin’, we could see it in his eyes. Frodo took the ring and put it on his hand. 
And then he and his sidekick Sam, they set out for Mordor-land. 
  
Boromir drew his blade but the Uruks kept a'comin. 
Though there wasn’t quite as many as there was a while ago. He blew his horn and we all came a-runnin' 
But by that time they had hobbits and now where did they go? 
  
Boromir drew his blade but the Uruks kept a'comin. 
Though there wasn’t quite as many as there was a while ago. Well I say “S” means Sauron and it’s very plain to read, But the others say they’re going where the Riders all drink mead.   
Five-eleven was his height, and one-ninety was his weight. 
And he somehow must have known that he had a date with Fate. 
The Ring filled his head with power-lust, he left good sense behind 
But when the chips were down it turned out he came through just fine. 
  
Next it’s run through the briars and run through the brambles That’s fine for Men and Elves with long legs and no chain mail. Those Orcs have a start and to catch ‘em will be hard By now they’re in to Rohan and halfway to Isengard. [repeat chorus]  

On the other hand, Dwarvish songs tend toward the melodramatic, at least when they’re singing about serious stuff and not about breaking plates.  So Gimli might have come up with this, instead:

The Ballad of Boromir (TTTO The Ballad of Ira Hayes [Johnny Cash])

Don’t call Boromir the Fair
He won't answer anymore
Not the handsome Númenorean
Nor the hero of Gondor

Gather round me people there's a story I would tell
About a brave young warrior you should remember well
From the land of the Númenoreans
A proud and noble band
Who held the Anduin valley next to Mordor land

Through the vales for two thousand years
The water kept Ithilien fair
'Till the Nazgul captured Minas Ithil
And turned it foul as Shelob’s lair.

Now Gondor's folks were angry
And warred for a thousand years
When a vision came to Boromir

Of an end to all their fears

CHORUS:
Don’t call Boromir the Fair
He won't answer anymore
Not the handsome Númenorean
Nor the hero of Gondor

There he battled near Parth Galen’s lawn,
Against seven score of Orcs
Few enough of whom would live to see another dawn

And when the fight was over
And Aragorn found him
Among the Orcs whom he had slain
Was Boromir the Fair

CHORUS:
Don’t call Boromir the Fair
He won't answer anymore
Not the handsome Númenorean
Nor the hero of Gondor


Boromir died a hero
Trying to save our band
But the Uruks took the Hobbits and lit out for Horse-Lord-land

But it seems there was something funny

Though Strider won’t tell us what
Still I can guess what he might’ve done
If Frodo gave him half a chance

CHORUS: Don’t call Boromir the Fair
He won't answer anymore
Not the handsome Númenorean
Nor the hero of Gondor

Boromir wanted the Ring;
He wanted it to save his home
He thought he could use and master it
Without turning bad to the bone!

He died this afternoon
Far from the land he fought to save
Some Elvish trinkets, his horn and a wooden boat
Were a grave for Boromir

CHORUS:
Don’t call Boromir the Fair
He won't answer anymore
Not the handsome Númenorean
Nor the hero of Gondor

Yeah, don’t call Boromir the Fair
But his land is just as doomed
And now we’re off to Rohan

Running through the twilit gloom