Is she in the appropriate grade for a 7 year old or did she skip a grade and in class with older kids?
If she is in a class with older kids, it may be a maturity issue (for her) or a jealousy issue (for the other kids), if the other kids feel threatened by her younger age and her higher intelligence.
If she is upset about this, I would talk to the teacher and find out who her friends are in the classroom and find out how her social skills are presenting. I would then make a surprise lunch date (don't tell DD you are coming) and go and see what the lunch situation looks like with your own two eyes. If she is indeed sitting alone, I would talk to the teacher about why this is happening at age 7. In our school, each classroom has two lunch tables that seat approximately 24 kids. Not only would it be impossible for someone to truly be sitting alone, it would not be allowed.
As far as recess goes, there is really no way to make kids play or interact with one another if they choose not to. I would role play with her at home to teach her some friendly social skills that will improve her chances of connecting with a friend at recess time. For example, I would role play with her on how to introduce herself and make a friend: Hi, I am Emily, what is your name? Hi XXXX, do you like to swing? Let's go swing together!
If you role play with her and she practices what you teach, in time it should improve.
