Install the latest Nvidia/AMD drivers. Set your monitor to run at 120Hz and at 1080p. Install the latest mouse drivers and/or firmware (if there are any). Go to your control panel until you arrive at the mouse options. Disable the "Enhance pointer precision" setting and make sure the speed of the pointer is at the 6th notch. Also disable any acceleration options in the mouse driver and set the polling rate to the highest available setting (usually 1000hz). You have mentioned a couple of Valve games which use the source engine. Make sure you have disabled V-Sync, disable mouse acceleration in game and enable the "Raw input" setting.
If you continue to experience lag, and you have an Nvidia card, you might want to try to reduce the "Maximum Pre-Rendered Frames" setting, but it might worsen your FPS. You might also want to try to change the USB port you mouse plugged into. If it's plugged at the front, or in a hub, try plugging it directly at the back of the motherboard instead.
EDIT: I didn't read you had an AMD card, so disregard any Nvidia related setting...
A couple of other things you might consider: try cleaning the sensor very gently or try another mouse from a friend in your rig to see if there still is any lag. If you are using HDMI, change your connection to dual link DVI or a quality DisplayPort cable.
Also, im not sure if there is any settings similar to this one for AMD, but for some reason, some people experience lag if they turn on GPU screen scalingin the Nvidia CP, so you might also want to disable any setting similar to that.