Having found that folder of my old lyrics and tried to remember their melodies, I've wondered how they sounded to other listeners than me. I used pop songs when I taught college classes on popular culture and workshops at local high schools. I focused on their rhetoric: the way we respond to the speaker in the song, the situation the song recounts, its effect on individual listeners. Just as we all have our own reactions to what we read or what we watch, we all have our own reactions to what we hear.
I played three recordings of the Lennon-McCartney song "Let It Be." Most familiar was the Beatles' original pop rock version; Aretha Franklin's was impassioned soul music; Joan Baez's was gospel-flavored folk music. The lyrics were the same in all three, which suggests that the meaning of the song was the same each time, but the singers' gender and race and the music they performed to varied. In class discussion students' preferences for one version over the others tended to be based on familiarity with the artist or the subgenre of popular music or their sense of the artist's sincerity.
This is a game you can play at home, comparing versions of songs in videos on YouTube—I just tracked down "Dream Lover" by Bobby Darin, Mariah Carey, Tanya Tucker and Glen Campbell, and Ricky Nelson, "Hello Young Lovers" by Frank Sinatra and Stevie Wonder, "House of the Rising Sun" by Leadbelly, the Animals, and Joan Baez, and "Heartbreak Hotel" by Elvis Presley and Willie Nelson. Or consider the music of three performers who just left us: Helen Reddy (she recorded two different versions of "I Am Woman"), Mac Davis (his song "I Believe in Music" was recorded by Davis, Helen Reddy, Perry Como, and many others), or Eddie Van Halen (look for an early song).
The other example I offered focused on how certain situations are presented differently in the lyrics and melody of thematically similar songs. Both Rod Stewart's recording of "Tonight's the Night" and Bob Seger's recording of "We've Got Tonight" are songs making a case for two people spending the night together, but the attitudes and the arguments of the male vocalists and their implied relationships with the women being persuaded vary quite a bit. Listeners might react to the vocalists' perspectives based on psychological or social preferences (and also to their possible preference for one singer over another), but if you read the lyrics without the melody, how would you react to either song—that is, to the message of the lyrics? If you heard the melody without the lyrics, in an instrumental version, how would you react to the song's attitude?
Only a few people ever heard live performances of my songs, always by me, so reading their lyrics provides little or no sense of their melodies. In poems we glean an understanding of pace and rhythm ("I think that I shall never see/a poem lovely as a tree" by Joyce Kilmer; "Whose woods these are I think I know/His house is in the village though" by Robert Frost). In my lyrics I can sometimes recognize the melody by reading the lines, like these from "Spending Time"
I know too much of wasted days
I know how much they cost
But counting all the empty hours
can't measure what I've lost
Or this chorus from "It Gets a Little Lonely in the Night"
It gets a little lonely in the night
It gets a little lonely in the night
By daylight I'm alright
But it gets a little lonely in the night
I recognize the stressed and unstressed syllables, the difference between iambic tetrameter and iambic trimeter lines from "Spending Time", the variations in feet in the repeated lines in "It Gets a Little Lonely in the Night." Emphasis and lack of emphasis determine the pace if I read them aloud. The texts of my lyrics tend to be metrical, but they aren't all obviously musical, at least to me. If you read both of these verses aloud, you might be aware of the metrical difference between them but be unlikely to intuit the melody underlaying them.
It's possible to find lyrics online with accompanying video or audio versions. If you read an unfamiliar lyric aloud, try to sense a melody, then listen to a recording to see how well your imagined song resembles the actual one. Your reaction might have something to do with how you're reacting to the lyrics. Those verses above trigger reactions in me; they open passages to memory and emotion that make me wonder how I'll feel about who the lyrics tell me I once was.