Please remember, it can take years and years to train a bird to free fly. There was one rather famous African Grey who was lost during free flying. His owner had done heaps of training with him and some training programs, he had flown him outside successfully but one time he didn't come back. Maybe he was frightened or lost, perhaps killed. As Wayne said, no bird is perfect and has 100% recall. Even if it has 99%, there is every chance that one time out of a hundred that he fails to obey, it will be outside and he will be lost. More often than not, pet birds, especially non-native birds (lovebirds are from Africa I believe), die after escape. Plus there is the possibility of being hit by a car, plane or helicopter or being caught by a bird of prey looking for an easy meal.
All I'm saying is please be careful! The bird is the one who will suffer.