Lirio translates to "lily", a beautiful and symbolic flower. It's a less common word in everyday Spanish songs, making it stand out.
In the lyrics, the phrase "flor de lirio" (lily flower) is used metaphorically to describe the person the singer is addressing. It evokes an image of purity, beauty, and perhaps a delicate nature, adding a poetic touch to the song's romantic sentiment.
Alfred García sings this to someone he can only describe by the things around her: "Tú, niña del sol de tarde / De las canciones viejas" ("You, girl of the late-afternoon sun / Of the old songs"), and then stretches the distance out to "De la Tierra hasta Marte" ("From Earth to Mars"). The questions he asks her are unanswerable on purpose — "Dime cómo huele el frío y de dónde viene el viento" ("Tell me how the cold smells and where the wind comes from") — while the thing he actually wants is plain and repeated: "Quédate conmigo hasta que se caiga el cielo" ("Stay with me until the sky falls").
The second half moves indoors, to someone at a window "con los ojos de nostalgia" ("with nostalgic eyes"), and being close stops being simple: "Que te busco y no te encuentro / Que te encuentro y no te entiendo" ("That I look for you and don't find you / That I find you and don't understand you"). By the last chorus the lines have been worn down to their first few words — "Quédate conmigo, oh / Cuando no queden días, oh" ("Stay with me, oh / When there are no days left, oh") — and the song ends by returning to the three lines it opened with, the sunset girl and the old songs.