How to make YouTube video with screen projection in background?
I don't think you can achieve this on a live webcast with only a laptop. You will want either:


a dedicated PC with an I7 or better CPU, appropriate video hardware (Blackmagic capture card or comparable) and software switch (Wirecast or comparable), or 
a hardware video switch (Blackmagic ATEM 1 M/E or comparable). 


Having purchased both types of systems in the past few years, the two options come out to about the same price, and I'm partial to the hardware solution.

Once you have the hardware and software in place, you can greenscreen the entire room, which creates lighting issues, or only a section behind the lecturer and use picture-in-picture to minimize the amount of space that the green-screen requires (and the lighting problems that go with it).

After that, the output of the laptop is just an input to the capture card or ATEM switch.