How to stop matchmaking for a particular game session?

So I have a game session where maximum 20 players can join. Players join through lambda response from APIs. The lambda checks for available servers and see if players joined are less than the max players that can be accommodated in the available sessions. if current players are less than max players the session can accommodate, the player will be allocated to the session. But for my game, I want the session to stop accepting players once the game starts playing phase from lobby. How can I achieve this. I am not using flex match or anything. Just Gamelift with API gateway and lambda.