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1.
If there is "no love lost" between two people, they have a strong hatred, hostility, or enmity for the other person, and make no attempt to conceal it.
Son, I'm aware that there's no love lost between you and your cousin Bob, but we'll be staying at my brother's lake house all week, so you'd better not ruin our family vacation by fighting!
by Eldorean May 27, 2009
 
2.
A sort of hatred between two rivals, whether individuals or teams.

Sometimes used by head coach and sports personality, Dave Logan, to describe the relationship between Mullen High School and Grandview High School Football.
There's no love lost between us. We both just do our thing and when we go, we go.
by MullenFootball September 09, 2010