It is difficult to say exactly what might be happening without actually seeing the bird.  There are two possibilities, though...

Lovebirds that have reached sexual maturity (usually at about 10 - 12 months of age) often show behaviors that mature birds looking for mates would show. One of these behaviors, especially for males, is "regurgitating."  This is when a bird brings food back up after eating it.  In mating rituals, pairs will feed each other this way.  It is their way of showing that they care about each other, and the male's way of proving that he is capable of helping the female raise babies if they have babies together.

Single pet lovebirds often still have the instincts of breeding birds.  Your bird may be going through the motions he/she would if getting ready to mate and have babies.  It looks a lot like the bird is throwing up when it happens, but the bird should be normal in every other respect.  If you observe your bird doing this, you will see that he/she will bob their head up and down a few times, and then the food will come up.  Birds will also sometimes do this when people are around, but then they eat the food again, so you never see it put on a perch or dish.

This is the most likely reason why you are seeing food like this in your lovebird's cage.  However, if there is another problem, it is important for you to have your bird seen by an avian vet as soon as possible.  Spend some time in the room that your bird is in and quietly watch him/her.  Observe your bird's behavior, and make sure that your bird acts normally in every other respect.  If your bird is sleeping more than usual, is quieter than usual, or is puffing up more than usual, these are all signs that something else might be going on and you'll want to see a vet ASAP.