There might be a little more to this.
https://www.ittsb.eu/forum/index.php?topic=343.0I would expect to be able to zero the LCR meter on two wires.
When troubleshooting these things I always rule out the leads, make the most direct short possible i.e. the component lead socket, or a bridged double banana plug. Try and zero to see if any difference. It pays to measure several small resistances or even a length of wire can work, shorting directly across to see if you can take various consistent measurements that make sense. Do this before you get to measuring capacitors. You might also want to use new batteries as well.
You can use whatever length leads you like but be aware they do impact the measurement especially when precise measurements are required, this is why shorter the better is generally a rule. While you can't totally eliminate the length of the leads affect on the measurement even after zeroing, the meter should still be usable even with a set of full length DMM leads zeroed out, especially for "ball park" measurements.
Be warned the LCR meter has no input protection against charged caps so is not so suitable (in my opinion) for constant in-circuit testing.
This video demonstrates how to perform a quick consistent measurement test, even though it's 4 wire measurement (modified test hooks) the same principles apply.