Here's one example, just to add to excellent examples above.
The song starts out in the POV of an observer. Here's what she sees and hears ...
Down the Lane, two men took shape in the fog. The big one on the right was upright but unsteady on his pins. The scrawny-looking cove on the left was holding them both up.
They were roaring drunk, which wasn't an astonishment in this street. They were singing.
". . . A pretty little oyster girl I chanced for to meet.
I lifted up her basket lid and boldly I did peek,
just to see if she haaaad any oysters."
Doyle whistled a long irritated breath out between his teeth. "That's 'im. Kendall's the big man on the right. Cup-shot, the both of them." He wiped his face with the sleeve of his coat. "Just what I need. Drunks with knives."
That is the POV character reacting to the song and to the singer.
The song itself isn't important.
What other people are thinking about and talking about is important.
Now we go into 125 words of scene description, ending with her comment on the song ... (still in the girl's POV)
Voices carried in the rain. She knew the song about the oyster girl. It warned a man not to trust a lass he met on the streets. Sadly true.
This brings us to a bit more dialog, the end of the chapter. The next chapter opens in the POV of the singer. There's 180 words easing us into the scene. While this other action is going on, we don't hear the words of the song. We just skip them. Then,
A fine day. An excellent day. More than enough reason to raise his voice in song, entertaining Katherine Lane.
"Have you got a little room that's empty and nearby,
Where me and my pretty little oyster girl may lie . . ."
He tipped his head back and let rain fall on his face. Heaven. He'd been back less than a week, home from the heat and stink of Corfu and points east. The cold pulled the poisons out of his lungs. It was good to breathe weather with some weight to it.
Adrian sang off-key, rapping his cane along the slats and shutters in time with the music. He wasn't drunk. Adrian didn't get drunk, not in his profession. He just couldn't sing worth a damn.
"While we bargain for her basket of oysters."
The brothels were islands of warmth and light floating in the fog. Upstairs, on the second floor, a couple of black-skinned ladies leaned out the window with their long oiled hair hanging down. The crimson and yellow robes across their shoulders were the brightest thing in these streets. Their little dark breasts were propped up naked on their arms, looking chilly. He looked like a man with coin in his pocket and sounded drunk enough to squander it. They called after him as he passed, raucous as seagulls, selling themselves. He waved and kept on singing.
"We hadn't been upstairs for a quarter hour or more
When the pretty little oyster girl astarted for the door.
She'd gone and picked me pocket and then down the stairs she tore."
The street bucked under him in a heavy groundswell. He rode it out. Didn't even stumble. Walking the bridge taught you to keep your feet. The captain had to set an example. Adrian didn't need to go propping him up. He didn't have to grin like that either.
"She left me with a basketful of--"
A woman's scream of terror and pain cut the fog.
The general idea is that the song is part of the ongoing action. It's part of the scene. Things happen around, and under, and behind it. People think about things while the song is going onward. They react to and think about the song.
The song itself sets out a timeline. All the other action has to march to the time it takes to sing the song. And you pick the length of the sections of song because they work with what else you're doing.
The rest of the stuff going forward determines which lines get 'heard' and which are just assumed to have passed
The whole song isn't here.
Now ... if you want to include every line of the song ... you can't do this.
Then you need big chunks.
Do you need the whole song for some reason?
Or do you really need the reactions to this singing?
*********************
So.
Lookit ...
Henry found the platform deep under ground, and waited. He heard the scampering of rats, and edged closer to the platform edge to watch them dart between the metal bars of the tracks, in and out of the daytime debris. The silence was profound, and the air stale and dead. He became cold, and clasped his jacket around him. As he leant back against the platform wall, he closed his eyes, and a tune popped into his head. He began to mumble along, hoarse and low.
'How strange it was, how sweet and strange,
There was never a dream to compare
With those hazy, crazy nights we met
When a nightingale sang in Berkeley Square.'
He sang the next verse a little louder, now lost in a faded memory, and reached a crescendo with the last line.
Maybe you want to mix it up a little:
Henry found the platform deep under ground. Rats scampered.. He edged close to the platform edge. He began to mumble along, hoarse and low.
'How strange it was, how sweet and strange,
There was never a dream to compare ..."
Rats darted between the metal bars of the tracks, in and out. In and out.
" ... a nightingale sang in Berkeley Square."
The silence around him was profound, the air stale and dead. He became cold, and clasped his jacket around him. He sang a little louder.
"Like a merry-go-round in a fair.
We were dancing ..."
Maybe think about what parts of the song have the most meaning.
