Is it necessary to perform the liftering function before applying MFCC to an audio signal?
No, liftering is never applied before computing MFCC because liftering is defined as a windowing operation in the cepstral domain. So you need cepstral coefficients in order to be able to apply liftering.
The effect of liftering is to smoothen the corresponding log magnitude spectrum, which can result in more robust recognition / classification results.
Also take a look at this question, and the references in its answer.