M.P.
As you said, girls are friends one day and on the outs the next but it's rare that all of her friends would be on the outs at the same time. I don't understand why she is sitting alone.
I've had playground duty for several years now and know that my granddaughter is sitting with a group of girls at lunch and having a good time but yet she'll sometimes say that no one likes her and she has no friends.
Is it possible that your daughter is sensitive and feels like she has no friends even tho she does? I would just keep telling her that girls are this way and that you know "she's a friendly, likeable girl and she will be OK." Be sympathetic but don't feed into the "poor me" routine if that's what she's doing.
It might help, if you haven't done this already, to spend time with her and her friends to see how they inter react. That way you can help your daughter understand where the other girls are coming from. My mother would tell me that sometimes the girls who are the meanest, in my opinion, were actually insecure and needed my empathy. This helped me to treat them nice even tho they treated me mean.
I've found with my granddaughter that she has discovered a couple of girls who don't play that game. You might encourage her to branch out and try making different friends. Have her invite a new girl home for a play date. There are no girls her age in my granddaughter's neighborhood. She frequently has a friend over or goes to a friend's house. For awhile she was in Y after school care and made friends not in her grade level. This helped. The broader her base of friendships the less likely she'll be eating lunch alone.
Encourage her to just pick and table and sit down so that she's not eating alone. Encourage her to chime in with the general conversation at the table. She will make new friends, this way.