Lobo has just received a contract to bring Supergirl in. He lures to an off distance planet(Mercury) to try and capture her. Lobo is not trying to kill her because he needs her alive for him to be able to cash in the contract. And as The Main Man stated himself "The Main Man has racked up some serious debt". Supergirl is not willing to kill either, as she is trying to prove that she is just as good and kind hearted as Superman.
-Lobo does have his chain and hook -Lobo can not die as usual, but the fight is until KO -Lobo can not clone, as this is current Lobo -There is no BFR -Supergirl has all her normal abilities -Neither character is willing to kill, but both are still going all out(as they usually do).