The lyrics to By2's song "Don't Go Away" express a reluctance to let go of a relationship, as the singer grapples with the confusion of happiness and heartbreak. The first verse conveys the singer's sadness upon the departure of their loved one, emphasizing how their eyes have reddened from the refraction of sunlight rather than from crying. They lament their inability to understand why happy moments dissolve so quickly and recklessly, and why the changing colors of autumn leaves signify the end of a relationship. The chorus acts as an urgent plea to their partner to stay and not leave them alone, as sharing life's experiences together is the only thing that makes it truly worthwhile. The second verse reflects on the growth of the individuals, how they have written songs and blogged about their experiences, and how their choices in life have been like green apples, full of naivety and youthfulness.

The song touches on the universal theme of love and loss and how it can be difficult to comprehend the complexities of emotions that come along with it. The use of nature imagery, such as the changing colors of leaves and melting ice cream, illustrates the fleeting nature of happiness and how it can quickly turn to despair. The chorus provides a sense of urgency, and the repetition of "Don't, don't go away" creates a sense of desperation for the singer's partner to not leave.