How can I improve the response time of a low pass filter?
You cannot greatly change response time of a low-pass filter by changing its' order. What you have to do is change its cutoff frequency - the higher the cutoff frequency, the faster the response.

Look at it this way. A low-pass filter removes high frequencies, right? And if you want the filter output to change more quickly it must contain more high-frequency components. You know, fast change means high frequency. So the only way to get faster response from the filter is to let more high-frequency signal through, and that means changing the cutoff frequency to a higher one.