Good question. I don't know the answer from experiment so I always like to think of the boundary conditions to see what may be likely. Two scenarios spring to mind:
- Sensor noise (chroma plus luminance) results in image smearing over a much larger distance than either the good or the bad lens can resolve.
In this case there wouldn't seem to be any point in using a sharper lens because the effect of sensor noise would swamp any extra fine detail it might deliver.
- Sensor noise is so small that the full theoretical resolution from all the pixels on the sensor is available.
In this case the chances are that the poor lens might deliver less detail so using the good lens pays off
So your question is really about where the cross-over point is between these two scenarios. Intuitively one would suspect that the effects of smearing from noise and lens combine. Indeed, if one looked at this in terms of MTF graphs where 1 is perfect and 0 is utter rubbish the final MTF of lens plus noise would be obtained by multiplying the numbers together (so if noise MTF were 0.8 and the lens MTF were 0.9 the final MTF would be 0.72).
Again relying on intuition (always a dangerous game in physics) one would expect that for the two scenarios above:
- As sensor noise is absolutely horrible to start with let's assume an initial noise MTF of, say, 0.4. Then the final MTFs from an "OK" lens with an MTF of 0.8 and good lens with an MTF of 0.9 are just 0.32 and 0.36 respectively. In practical terms you wouldn't see any difference as both images would look horrible unless they were displayed as thumbnails.
- For virtually no sensor noise let's assume the MTF for noise is 0.95 - hardly a factor. Then for the same pair of lenses one would see MTFs of 0.76 and 0.855 respectively. Virtually all the extra performance of the good lens is delivered in the final image
Phew! That was arguably a lot of mumbo jumbo but, hey, it's written now so I may as well leave it in place to be shot down in flames as appropriate.
So where's that crossover point you wanted? I'd argue that it doesn't exist in practical terms.
The sensors on all DSLRs, and probably most compacts and superzooms though their lenses are fixed at the design stage, are capable of achieving low levels of sensor noise at the lowest ISO setting. So unless you never
shoot in good lighting you can always get benefit from a better lens - this is scenario 2 above.
Of course if you always shoot in poor lighting with consequent high levels of sensor noise then scenario 1 applies and you could get by with a poorer lens. Except, of course, that a better lens may
also have a brighter aperture allowing you to also reduce the ISO so you win because the brighter lens effectively improves the sensor noise MTF.
Maybe if one always had to shoot in bad lighting one could argue that investing in sharper (as opposed to brighter) glass wouldn't be worthwhile if smearing from sensor noise (expressed in pixels) is greater than, say, twice as large as the smearing (loss of resolution) from the lens. But that's total guesswork
P.S. For more on MTF curves check out this article