Using gnome-tweak-tool, I specified my Thinkpad X220 laptop to suspend when the laptop lid is closed (for both AC and battery). Everything works fine when I close my lid if an external monitor is not connected.

When an external monitor is connected (my typical setup at work), the laptop will not suspend when I close the lid. The display will turn off, and that's it.
The same is true if I specify the action to be Shutdown when then lid is closed. That is, the display turns off and the system never shuts down.
The only way to suspend/shut down the laptop when I close the lid is to first disable the external monitor and then close the lid. I want to avoid doing this.

Note that even when an external monitor is connected, suspending through the Gnome menu or via pm-suspend works fine, but I want to be able to suspend/shutdown when I simply close the lid.  Something is not being triggered when the lid is closed or an error is occurring, and I don't know quite where to look.

Note also that disabling the xrandr plugin for gnome-settings-daemon and using an external tool, specifically arandr, did not make a difference.