There are three students named Gilliam in the roster of the Mordecai school I compiled in 1996: Eliza, Lucy, and S. Gilliam. The are not at the school long--each girl for a single term. Eliza and S. were at the school during its last term in 1818, and Lucy Gilliam was there in the first term of 1816. Ed. Anderson is the adult name that might be attached to Eliza and S.; Mr. Hardaway might be the adult name attached to Lucy Gilliam. (I say "might" because I put a question mark after each name in the appendix of my dissertation, so I must have had reason to be unsure.)
So, that's not much to go on. But let's see what online resources can tell me in 2024.
There are a couple likely candidates for Lucy Gilliam. There's Lucy Ann Gilliam born in Petersburg, Virginia, in 1799--that's exactly the right time and place for a Mordecai girl. She's the daughter of John Gilliam and Hannah Sampson. But there's also her cousin Lucy Skelton Gilliam (1804-1872), daughter of James Skelton Gilliam and Mary Feild, also from Petersburg, Virginia. Their grandmother was named Lucy Ann Skelton Gilliam--here's a portrait of the elder woman at Colonial Williamsburg; she was related by marriage to Martha Wayles Jefferson.
I don't know if our Mordecai student is either of these girls, but both are the right age and location and class to be possibilities. Lucy Ann would have been 16-17 in 1816; Lucy S. would have been 11-12; the latter is closer to average, but both are in plausible range.
However, from what I can see, neither girl had a sister Elizabeth who was the right age to attend the Mordecai school in 1818. Elizabeth was a common name, of course. and there were several in their families, but none born in the target range of 1805-1810.
I don't know where to start with S. Gilliam. S is such a tricky letter in manuscript sources; maybe it was a J. Maybe it was an F. Maybe even an L. I can't go look again, so I'll leave that alone for now.