I have no experiance with this plan / kit, but I have quite a bit experiance with using lock-in amplifiers and I have build my own version of a lock-in amplifier. My version looks quite different though and has plenty mistakes to learn from.
There are a few issue with this plan:
1) The outputs are directly from the amplfiers. To avoid capacitive loading to the amplifiers it is a good idea to have some 50 or 100 ohm in series to the outputs.
2) The usualy way is to used the output DC coupled. So the capacitor for the output is a thing to drop - a good place for one of the 50 ohm resistors.
3) The amplifier is rather basic. The higher gain setting of more than about x 1000 have a limited bandwidth. This may be just a little much gain for one stage. It limits the use to relatively low frequencies (e.g. 1 kHZ or less). This can be OK for some uses, but could be an issue for others. In many cases one may have a custom pre-amplifier for the signal source anyway. A protected power source may be substitude a better amplifier to some degree.
4) a point missing are a way to detect clipping, like 2 comparators or simple diode / capacitor detectors for the peak values. Not absolutely needed but a nice to have point.
5) Another usefull and commonly found part with the input is a mains frequency notch filter, possibly also the 2x mains.
6) The output filter has settings for rather low time constants - these make little sense with an amplifier that is limited BW. It is more that a longer time scale could make sense, though today a medium time scale like 100 ms and than digital averaging low pass filtering at the putput would be a good way. So the longer time constants may not be that important. Using electrolytic capacitors with the filter is not ideal. At least the 100 ms range should get way without electrolytic capacitors.
7) depending on how the output is read / displayed one may want more output gain as on option (e.g. with a signal with low SNR)

The reference input is directly to the chip - this is kind of a start to add a reference section there. The reference section ideally includes quite some circuitry, so a start, but yet quite ready. One usually wants a bit of protection and signal forming, so that one can start with a crude signal and still get a reasonable sine or optionally square wave with defiened amplitude. Ideally one would also get a fine phase adjust with a precise 90 deg. jump option (e.g. via a PLL). The 90 deg. phase shift part is very handy to adjust the phase. Quite often the ref. side also include some simple generator option (e.g. comes easy with a PLL or so).
Old style analog lockin amplifiers are to a large part replaced with digital solutions. So digitize the signal with enough dynamic range (e.g. a sound card or similar) and than do much of the LI technique digitally.
For the experiments that can be done, there are a lot of optics experiments (e.g. look at absorbtion or reflection). This can be with modulated LEDs as a light source or a mechical chopper.
Another nice experiment can be a field mill to measure electic fields. Utrasonic , acoustics is possible to, though it may need a higher BW amplifier to not get too much phase shift from there.
LVDT mechanical displacement sensor can be read out with a lock-in. Similar DMS can use a carrier frequency amplifier, which is a lockin pluse oscillartor for the reference.
A LCR bridge could use a lock in amplifier - though this really needs the phase shift part.
I have done photo-acoustic detection of light: so use a microphone to detect the pressure rise from modulated light to heat up some gas (e.g. water wapor to absorb 950 nm) or solid surface.