I'd be thinking losses in the electrolytic caps 100uF+ 10uF. Maybe one is in the wrong way. Maybe they are different parts (brand type) to the ones you previously tested.
Ok. I think the ways of both are correct: Reversed to each other. However I think I used (as far as I remember) the exact same caps as I am using now on the circuit. In a first stage of testing I used a single cap with a different value, but I think I remember testing with these two the way they are now.
One of the electrolytic caps around the wrong way might do it. So too could be the fact to are using two different values in series.
I think both of these problems *could* be related to the electrolytic caps.
Hm... I get it. It all comes down to the 2 electrolytic in reverse series.. Which is something I didn't want to happen because I can't really explain how they work, except for saying that this is widely used.
Again, I'm 99% sure they are the right way. But on saturday I'll open the circuit and check that. It's just I do'nt want to hang with the open circuit till there..
Anyway here goes the real schematic on EasyEda:

We can see that they are in the right direction, but let's see if I didn't screw up on assemblying.
Ticks are fairly common with circuits that have an LFO.
I'd say two common causes would be:
- using dual/quad opamps where different opamps in the same package are used for audio and for the LFO.
I think there is no dual op amp here used for LFO and audio at the same time, as far as I see on the EasyEda schematic..
- Not enough bypassing on the supply at the LFO. Try adding, even temporarily, a 100uF cap across the pins of the LFO (specifically the Schmitt trigger opamp). If that doesn't work the next step is to put a resistor between the main power and the power for the LFO circuit. Something like 10ohms to 100 ohm. You will need to keep the 100uF cap on the LFO power. The idea here is to isolate the LFO power.
Fair enough.. it seems something like the P90 LFO that has that capacitor and that resistor that you said were just controlling the rises/falls of the schmitt trigger (that weren' that important). I guess I'll do it on the LTSpice simulation, because my circuit is already soldered. I would just solder anything on top if I were sure that it would work. If not, I'm afraid of damaging the circuit.
Just for the record, what's the "main power" and the "LFO power"?
There's other possibilities like the LFO wiring is near or touching audio wires in the enclosure, PCB tracks on the LFO are close to audio tracks. Ground tracks sharing LFO and audio signals.
Interesting cause ground tracks most probably are the same.. But the wiring seems to be correct, even though I will double check it.
Another one is the LFO is causing fluctuations on Vref or Vbias and that is injecting click into the audio; as the any variations in Vref will appear at the audio output.
This is what used to happen in the P90 LFO, in the simulations actually. I tried to isolate the parts as much as I could with all those op amps on the LFO for this not to happen but I guess it's not that easy after all.