Sounds to me like you're not looking for an LCR meter which measures inductance, capacitance and resistance (impedance), but rather a semiconductor tester or curve tracer. I believe there are some DIY or hobbyist-level designs that you may able to build for a few hundred dollars, but otherwise expect to pay more.
You may be able to do something with a programmable power supply with computer connection and software (see for example
here), but it definitely won't be portable or very convenient. There is also a topic about an open source source measure unit (SMU), but I don't know how finished that is.