It seems that your grandchild may not be getting a sibling by birth or adoption. It is also clear that the parents are very busy, but she is indeed lucky to have a caring and aware grandparent!
Loneliness in such a case can mean many things-either the child feels a lack of playmates or that she suffers from lack of parental attention. Once you are able to identify the exact nature of the problem you can try certain suggestions.
a) Try talking to the child as to the exact feelings she has.
b) Keep communication channels open with her so that she may feel comfortable sharing her thoughts and feelings with you.
c) Try taking her to a park or for a walk where she can meet age mates and encourage interaction.
d) Share your concerns with her parents and involve them in taking steps to help the child.