"He is the love of her life."
Translation:Er ist die Liebe ihres Lebens.
well, you can but it sounds very awkward. "Die Liebe meines/deines/ihres/seines Lebens" is a common phrase
Genitive singular case often ends in -s for masculine and neuter nouns.
Here, you have a neuter noun (das Leben) and it's in the genitive case (des Lebens / ihres Lebens) to show that it's "OF her life".
These "of the" relationships can usually be reworded in english:
The door of the car.
The car's door.
Die Tür des Autos.
The s on car's and Autos is functionally the same.
It's not the usual phrase but "... her life's love" is another way of putting it.