Should I run input or output over the LFO?

[Hal]

I can't avoid it - which one should pick up fewer clicks?

[Paul Perry (Frostwave)]

The output is much less prone to pickup of noise.
The rule is, the higher the impedance of a signal point, the more likely is interference pickup. And, the lower the signal level, the more likely any noise pickup will matter. Both these points say the output is less prone to pickup.
But, in my experience, usually if there is click pickup from a LFO, it is coming thru the power rail, and you will have to decouple via a 220 ohm resistor & an electro.