Look across Lake Michigan from The Michigan side towards Chicago or Milwakee. Some days you can see lights and/or part of the skylines. Some days you cannot. Refraction.
When you look across Lake Michigan, the reason you can or cannot see the Chicago skyline is because of fog or the height of the waves.
Waves. On the Great Lakes. Blocking view of a city skyline.
Some big waves can develop on the Great Lakes for sure - unrelated, but check out the info around the "White Hurricane" of 1913 : 35-foot waves!!
https://en.m.wikipedia.org/wiki/Great_Lakes_Storm_of_1913
But those are never going to be the reason someone cant see Chicago unless you're standing in the swash zone along the beach. The reason the skyline is transiently visible across that distance is from refractive effects producing a mirage. Just google "Chicago skyline from Michigan" for some beauty pics and several articles
Actually, you write as if I would know nothing about it.
I live quite nearby and enjoy cycling along the southern tip of Lake Michigan from Chicago all the way to St. Joseph, MI.
Waves and swells can certainly block the view of of the city skyline and more often than not, do exactly that. I have no clue what you are writing about and that is due to the fact you have no clue about what you are writing.
As far as the weather is concerned (in the area between Chicago and Southwest Michigan) it is more often than not, cloudy over that area of Lake Michigan.
These are indeed the reasons for the skyline being out of view of observers.