I mean, If you go to play with the other kids, and they want to do something you don't enjoy, and what you find fun to do no kid does... Does it mean you are lonely?
When I was a kid I loved to play sports like the other kids, and was very good at it, so I was very social,but I also loved reading tons of books and mathematics. Most of the other kids did not.
When you read Kant, Descartes, Stefan Zweig(in german) books that tell you how to raise a kid while you are the kid!, Asimov (in english), Feynman ... all the other kids behavior becomes so childish and stupid.
You could be alone while standing with other people.
For me the fact that Lisa Simpson is alone is not that she is lonely, but the consequence of being unique while other unique people live far away.
I got to find and regularly meet other people like me only as an adult. Most of them are really successful now, but most of them also lived Hell in the school days.
They were alone, but they are not lonely.