The answer to the question above would be that the appositive in the sentence is the following one: New York University and Columbia University.
An appositive is a noun or noun phrase that renames a noun right beside it. Nonessential appositives appear separated from the sentence by means of a comma, a hyphen or paranthesis in order to indicate that the information they provide is not essential to the meaning of the sentence. In this case, the appositive phrase specifies the schools that Lillian attended.