Is it possible to run it with lid closed... Depends.
There is one way to do it and may be another.
SOME laptops you can set (usually in power options off the control panel) how they respond to a closed lid (Do nothing, sleep, hibernate, turn off monitor) you want turn off monitor but otherwise keep running.
Now you need a Wireless or wired keyboard and mouse, If it has PS/2 Connectors I have KB and mouse but I like wireless and USB.
And an external monitor (Most laptops have provisions but if yours does not and has enough USB ports. go-4-that route)
And that is all there is to it, very easy.
IF you can not find an option to keep it running lid closed.........
Find the tab on the lid that presses the switch and .. Well.. I think you can figure it out.. I DO NOT recommend this save as a last resort.