Love and grace are closely related things. Showing someone grace means showing them favour, goodwill.1 Loving someone means you desire the best for them.
In theory, someone could show another person grace without loving them. However, you cannot truly love someone without showing them grace. When it comes to God, he shows favour because he loves. I suppose you could say that God’s love is the motivation behind his graciousness.
Notes
1. For more on grace, see the answer to ‘What is grace?‘.