I'd be happy to help if you like.
Not sure if you already have the additional screen etc but, (
without trying to sell you something), I do have 2 x pieces of equipment which could help.
A Monitor -
HP 2011x 20-Inch LED Monitor - Black - Talk of the Villages
A "Docking Station" -
Toshiba Dynadock U3.0 Universal USB 3.0 Docking Station - Talk of the Villages
Once the second screen is attached, there is an option in settings under the power section on what to do when the lid is closed. All you need to do here is to select the Option to do nothing.
Again, happy to help at no charge if you want to contact me.