LEA stands for Local Education Agency. Basically it's a another way of referring to the 'school district'. In an IEP meeting, the LEA is the representative of the school district that referred the student to special education services, and pays for them.
When you see LEA Representative on an invitation for your child's IEP, it basically refers to one of the licensed professionals at your child's school who knows your child and is knowledgeable of the IEP process.