Can't say much without a soil test. Sulfur is used to acidify soil, but cukes will tolerate some alkalinity. Leaf yellowing is indeed a sign of overwatering in cukes (as is powdery mildew), though I'm not sure if that is applicable only to older leaves.

In the picture you show, the leaf doesn't quite look yellow, but with green veins. That's chlorosis, which is a form of anemia. You see it in old leaves. Chlorosis is a sign of iron or magnesium deficiency, I believe. Again, soil test is needed. Now, if the soil is highly alkaline, it may interfere with iron absorption, so that may be where the recommendation for sulfur comes in.

You can do a search online for nutrient deficiencies in cucumber plants and compare pics for yourself. But I would agree that it looks like iron or Mg is low. That may be due to or made worse by over watering.

A soil test or even better a leaf analysis would give more conclusive answers. But you could experiment with some foliar sprays. For Mg some Epsom salts dissolved in water is a good source, and relatively cheap and available (at least here). I forget the recommended dilution but it can be looked up fairly easily. Chelated Fe is also available if the Mg does not help.

Depending upon the urgency of the problem and if you have time to experiment and see if these can help, trying foliar supplements would be the easiest and cheapest avenue.

It is normal for the older lower leaves to turn yellow and die, as long as it is not caused by disease.

Yellowing also may be caused by lack of Nitogen. Over watering dilutes Nitrogen and leaches down, beyond the reach of root system.
Manures are good source of nitroge.

Seysonn

This is not iron or nitrogen deficiency, but probably magnesium deficiency.

I am leaning away from Mg given that the chlorotic (yellowing) symptoms are typically more "blotchy" looking and can be raised or puckered, and more vibrant yellow. Mg Def also begins on lower, mature leaves for what its worth. It looks more like Fe or N Def to me given the "paler" look to the chlorosis (S deficiencies are much less common, but are very similar to N Defs) the differences being that Fe Defs start on the upper, youngest leaves and can progress downwards and N Def start on lowest, mature leaves, sometimes N Defs can also exhibit a reddish cast, but not always. S Defs differs from N in that typically the entire plant will exhibit the symptoms you show on the two leaves and not just one portion or another. Hopefully this clarifies a little bit of the differences between all of these deficiencies.

Could this be zinc deficiency?