So sorry to hear about the loss of one of your lovebirds. This is a difficult loss for both humans and birds alike, particularly since your lovebird was 13 years old.
The fellow lovebird probably is sad that its friend is no longer around. Lovebirds bond very strongly to each other, and the loss of a friend is not always easy, especially when there are no other bird friends in the house. However, it is not necessarily a good idea to bring a new lovebird into the group.
Your lovebird misses the other one because they were bonded and knew each other for many years. It is very possible that a new lovebird would irritate your bird, or that they would not get along. Just because two birds are lovebirds does not mean that they will necessarily like each other. Every bird has an individual personality and sometimes these personalities don't mix well together.
In order to help your bird overcome its sadness, try spending some more time with your bird. If your bird is not a hand-tamed pet, you can sit near the cage and talk to the bird from a distance. This added attention may help ease the pain of the loss of a companion. Buy some new toys and introduce them to your lovebird. Having something to do with its time will also help get your lovebird active once more. You can also rearrange or move the cage, so that your lovebird is in a new setting.
I would not recommend getting another lovebird and putting them in the same cage. Older lovebirds (like yours) will be either cranky or very mellow towards a new bird. The new bird may try to take advantage of the mellow behavior and start pushing the older bird around. Or, the older bird will be cranky about the new intruder and try to hurt the new bird. Lovebirds DO generally like the relative company of another bird, so you could get another lovebird and put them in different cages in the same room. That way, they can talk to each other, but not be too close in case they feel the need to fight. Of course, when considering this arrangement, it's best that the owner actually WANTS another bird. If not, then you will end up feeling resentful of the addition and the need to feed and clean another bird. This is not a good situation to be in.
Your lovebird CAN get over the loss of a friend without the company of another bird. And if this is the best arrangement for you personally, then helping your bird get through its grief is definitely a better option than bringing another lovebird home.
Jessica
Love 'n Let Aviary
www.lovenlet.com