The only ~$200 handheld LCR meter that doesn't make the assumption of lossless (pure) inductance or capacitance that I know of is the Extech model 380193 LCR Meter. I have one, and it works well. It measures L, C, or R at 120 Hz or 1000 Hz (but not R at DC), and for L and C also reports parasitic R.
The B+K model 875B LCR meter did not work for me because they only worked with very pure inductances. I have heard that the Wavetek meters also have the problem. The test is to take a relatively pure inductance, like one winding of a power transformer, and put a potentiometer in series. Does the reported inductance vary as the series resistance is increased? With the B+K, it just explodes, with the indicated inductance becoming a large factor bigger than the true value, so a 2-henry inductor was reported as 45 henries. Complete nonsense, rendering the meter useless.
Note that one-frequency and two-frequency LCR meters cannot detect self-capacitance in an inductor, or self-inductance in a capacitor. Only parasitic resistance can be detected.
Joe Gwinn