Operating system used in this tutorial: Linux Mint 16 Cinnamon 32-bit
How to get laptop to "Do Nothing" when the lid is closed on Linux Mint.
1. Navigate to Menu -> Preferences -> Power
2. A Window pop up shown like above picture, now in the drop down list option of "When the lid is closed" chose "Do Nothing".
3. You are done!
PS: I am assuming that you have VNC connected to Linux Mint and now close the lid of the laptop, the screen may lock you out but just log back in and you will be fine! Enjoy!