The idea is already implemented different bridge measurement circuit by using same sensor in other arm of bridge circuit. About your specific application of LCR meter, you have to find compensation circuit with same concept as bridge but it is very difficult for every new measuring impedance .

Sir, we were looking for an idea which would not require adjustment for every new measurement to be taken, the same problem faced when using bridge circuits. 

Can we possibly use another circuit idea which works around this problem? (Using a microcontroller was an idea, but the complexity of the circuit implementation seems high in this case)

Thank you

The impedance matching circuit should be adaptive to unknown impedance. The question is how to estimate unknown impedance. Hypothetically concept will work but getting its implementation is difficult.   

You can measure it in two parts. Measure the phase by a standard phase detector circuit. Measure the impedance by inverting amplifier.

Dear Meghana,

welcome,

i know that i came late to your question, but i developed a computer based method to measure the impedance, it relies on the four voltmeter method that can be implemented by a measuring circuit with a sinewave oscillator and a data acquisition card from national instrument and PC or Laptop. For the dtails of the method please follow the link: Article Four Voltmeter Vector Impedance Meter Based on Virtual Instrumentation

Best wishes