The city puts volcanic cinder down for traction on ice, and when it rains the wet cinder goes up into my chain and turns into a gritty mess on any lube I use other than the waxy ones (and I have my doubts about the waxy ones).

I take my chain off and spray it with WD-40 as a solvent.

After it soaks for awhile, I wash it in my kitchen sink with soap and hot water.

Sometimes I let it soak for awhile in the hot soapy water.

Then I spray it a again with the WD-40 to displace the water, wipe it down very thoroughly with paper towels, and lube it with whatever seems like the right lube at the time.

In the absence of rain and cinder, I don't clean or lube my chain.
It can go all summer without any more than a wipedown.