His relationship with Lily was used as a way to show a different side of the character.

You want to stay here with Lily and wait for the phone to ring?

I spent a last two days with my parents and Lily.

He'd originally taken up with Lily because both of them were bored.

He falls instantly in love with Lily, the most modern and beautiful daughter of the family.

You stay here with Lily; I can find my own way out.

I'll just hang out with Lily until you get home.

Tyler's got nothing to lose by flirting with Lily, so he does.

Fool that he had been, he'd hoped to find happiness with Lily.