You can enable or disable Layby option from the "Admin" -> "Settings" -> "LaybySetting".
You can predefined the minimum total price for Layby, so the shipping cart won't display Layby option if the total price is lower than the value.
In the customer invoice, There will be three more line displayed.
And you will also see an "Money" icon shows in the order/invoice list if it's a Layby order.