THAT is the EXACT same story I had. I had two female mice and one died and the other one seemed distraught and lonely, so I decided to try to introduce another new female mouse to her.
It worked at first and we were really optimistic and glad. We learned from a internet site that if you put a dab of vanilla a strong over powering scent on each of their haunches it might help to introduce them. Because they don't want to hurt each other if they smell the same. It would be like hurting family. A good way to get the right amount of vanilla on them is you dab it on a washcloth and gently rub their haunches with it. They smell each other right on the fur on their rump. not their butt, but their rump. the reason it seemed to work at first is that female mice unlike male mice, wait for quite awhile before they fight. When there was a wheel in their cages it would distract them enough that the would get along perfectly, but if we took that out the first mouse would bite the new mouse. It was really sad because the new mouse clearly wanted companionship, and the other mouse wasn't letting her be friends. A few tips you need to know if you introduce them is that they need to be in a Neutral environment meaning it has to be completely free of both their smells. When getting the mice you need to get a mouse that seems to have a VERY different personality it is too hard when you have two dominant mice. When you introduce them you have to keep them under Extreme supervision for an extended amount of time because females wait to fight. It can be done but it is really hard. I ended up having to get a new aquarium, and cage set up, because it didn't work out. You just have to know what you are getting in to. I know how hard it is to see your mouse sad and lonely, so I understand. It is worth a try, but if they seem to be looking like they are going to draw blood I recommend not putting them back together. And if they do draw blood don't put them back together.
I hope whatever you choose works out.