I've been fascinated by the NE567 since I got the book "Minispione IV" - the venerable little IC is a more bare-bones version of the popular CD4046 PLL chip + comparator in an 8-pin package.
Lock-in measurements are interesting because they enable detection of weak signals below the noise floor. This is achieved by effectively rejecting uncorrelated noise and by creating a very narrow bandpass (it's a really nothing more than a mixer, followed by a crazy low pass filter, e.g. with < 10Hz BW).
The oscillator pin (6) can be driven with the oscillator voltage (pin 2 / 6) of an NE555. An experimental setup is modulated by the NE555 output (classic lock-in measurement) and the return signal is capacitively coupled to the signal input pin (3).
The output filter pin (1) presents with a voltage that drops monotonously with the synchronous detected measurement signal. The former loop filter pin (2) should present Vref? - at least for purely in-phase detection.
I eventually did put this together just to see it running:
blue: 22nF ceramic caps (used for supply bypass, NE555 pin (5)), NE567 coupling to pin5 is done with 150nF, output and loop filter caps are 10µF electrolytics. The NE567 supply is further filtered with 1µF/100V + 10R metal oxide film resistor. The pots and remaining resistor are there to adjust the NE555 frequency and attenuate the sample signal.
In my opinion this circuit is nice and simple and illustrates well the principle of synchronous detection and the general operation of the NE567, while in a broader sense provides a different tangent to phase-locked loops and lock-in amplifiers.
If you want a light barrier, high noise high resisitivity or low signal detection experiment as a weekend project and learn something about lock-in amplifiers along the way, this might be a fun thing to try.