A writer wants to show that a character is attracted to someone, but it's too soon in the story for The Big Damn Kiss or even a Love Confession.
They have a few choices. They can have the character state, plainly, to a third party, their interest. The writer could have them tell the audience, Breaking the Fourth Wall. Or, if they're going for subtle, they can have them bite their lower lip coquettishly.
In real life, there are numerous reasons why a person might bite their lower lip. It is associated with anxiety, and numerous experts on body language will state that it is meant to show holding back thoughts that one doesn't wish to voice aloud, and while that does include thoughts, fiction tends to focus on this aspect.
An Always Female trope, no matter which characters do this, it can suggest a sort of innocence or youthfulness to the attraction.
Related to Nervous Tics.