Justice is a good place to begin. "An eye for an eye" continues with "a tooth for a tooth". I am not sure it was even meant to be taken literally. The lesson is, if someone knocks out a tooth, justice is not taking someone's eye. Let the restitution fit the situation, not surpass it. In today's world, how many file frivolous lawsuits over something relatively minor, essentially asking for an eye in return for a tooth?
"Love your enemies." Biblical language is helpful here. An enemy is someone you hate, someone you are jealous of, someone who you envy. The instruction is turn away from your own hate, jealousy, envy, etc. and learn to love instead. What if it is someone who is jealous, envious, and hateful towards you? Do good to them.
So much of the time the Bible is talking about every day, interpersonal relations. And too often our thought of an 'enemy' is only those who want to rob us, take what we have, even kill us. Therefore, an immediate response is, "I have no enemies." And, as we have no wish to rob, pillage, and plunder anyone, we think we have no enemies.
Once we turn our minds to pettiness that arises in everyday relationships, "Love your enemies, and do good to those who hate you," makes a great deal of good sense.