Sridhar,
I do not think you will be able to do what you are asking. The OS controls the serial port hardware. If the UART has its own oscillator, then you have two clocks which are not synchronized to deal with. I have never seen any method of accessing either clock form within LV. Further, since RS-232 is an asynchronous communications method, timing is not defined beyond the frame of one byte.
Perhaps if you described your measurement problem in more detail, someone could offer a solution. Information we would need include: minimum and maximum frequencies, waveform and amplitude, accuracy and resolution, how often are measurements required, and anything else you think might be relevant.
Lynn