Summertime Sadness is another/one example of a deep song. The complexity of the emotions of the song.

the happy yet sad meaning of the song.
Ride is also amazing and deep. It's not about Riding a bike??

it's about breaking free from what's troubling you.
National Anthem criticizes the money and power Obessed society.
Radio is also deep about the bitter sweet taste of fame.
Born To Die is about a doomed relationship but it can be interpret in many ways.
Young And Beautiful is also lyrically deep about reassurance if someone will love you or not when youre old and ugly lol. It's not a shallow straight forward song like most think. It's very honest and vulnerable.
Angels Forever, Black Beauty and most of her unreleased has a very deep complex subject matter.
I can go on and on forever lol.