Okay kiddo, so sometimes when grown-ups have to make an important decision, they ask other people to help them decide. These other people are called assessors.
Now, sometimes these assessors can be regular people like you and me, who may not be experts in the field that the decision is about. They are called lay assessors. Lay means not trained in a special way.
So to sum it up, a lay assessor is a normal person who helps make a decision about something important, even if they are not an expert in that area.