Generally speaking, the response time restricts how quickly pixels can change colors which translates into motion. While monitors may be rated at 2ms, 5ms, 6ms, etc... those numbers represent theoretical timings. Even "2ms" rated monitors can have response times as slow as 40ms or slower depending on what is being displayed.
I would guess that LCD monitors typically have average response times between 15ms to 20ms. There are 1000ms in 1 second, therefore a monitor that can average 15ms response time means it can theoretically display up to 67FPS and 50FPS if the average response time was 20ms.
A 120Hz monitor will not improve frame rates. I is generally used to improve image quality (at least for HDTVs). Basically in a 120Hz HDTV an internal processor takes the 60 frames it receives per second and "doubles" it by creating an "in between frame" or interpolated frame.
Example: The HDTV receives a video stream from the Blu-Ray player. It gets frame 1 and frame 2. The HDTV internal electronics looks at the difference between frame 1 and frame 2, then it creates frame 1.5 to insert between frame 1 and frame 2. The HDTV then gets frames 3 and 4 at which point it creates frame 3.5 and drops it in between the previously mentioned frames 3 and 4.
120Hz monitors are just beginning to hit the market. I honestly have not researched them, but if it works the same way as an HDTV, then it will create input lag because video cards are designed to transmit video signals at 60Hz. Video cards need to be redesigned to output at 120Hz, but that will take time because any such changes must be approved by a "video standard" committee before the video card manufacturers will adopt 120Hz transmission.
Input lag is the delay between the time you press a key or move your mouse and you see the results on the screen. No manufacture will list input lag. Period. All LCD monitors have some level of input lag. Some more than others. Some have may be as low a 10ms, my NEC LCD2690WUXi has been rated to an average of 30ms (or almost 2 frames), others like the Dell 2409WFP (revision A00; known as the first version) have input lag of 50ms.
The only way to test for input lag it to place side by side a CRT monitor and a LCD monitor, and both are displaying a timer which can display milliseconds. Take a good camera and take a snapshot at very high shutter speed and there you go.
How input lag is too much input lag? This is done by assuming that the average person see 60 frames per second in real life. Again, there are 1000ms in 1 second, divide 1000ms by 60 frames per second and that gives you 16.7ms. Therefore for every 16.7ms of input lag 1 frame will pass between your action and what is then drawn on the screen.
Based on the above a 120Hz LCD monitor will generally have higher input lag than a 60Hz LCD monitor because it takes time to interpolate an "in between" frame to improve image quality (well at least image quality of movies and videos).