The identification of the client where a lawyer is hired to represent an entity such a a board of education is often a difficult problem. Lawyers are responsible to be clear with their clients about who is a client and who is not. Often asking the lawyer is the only way to identify the client or clients in a particular instance. For example, if there is a dispute between the school and a parent, the lawyer is likely to consider the teacher her client. If the dispute is between the school and a teacher, the same lawyer probably does not consider the teacher a client. If a school board member is charged with embezzling money from the school, the lawyer may say that her only client is the school district because she does not know who else might be responsible for wrongdoing.
DISCLAIMER: I have not agreed to be your lawyer or to give you any legal advice. This response is for information purposes only and is not legal advice. For legal advice you need to find a lawyer who will agree to represent you in this matter.
"Education lawyer" is another way of saying a lawyer who practices in the area of education law. Who the lawyer represents depends upon who the lawyer's client is. We can't tell who the lawyer's client is, because you haven't given us enough facts.
Just general information, not legal advice. Good luck.