You'll get varying opinions, depending on what minimum standards folks go by, the weather conditions of their area, and how they view their chickens. I go by the LF - 4sq. ft. each for housing and 10 sq. ft. for run space, and Bantams, 2 sq. ft of housing and 5 sq. ft. of run space. Of course if you're in an area that doesn't get winters, then you can get by with a little less housing space. But in your case, your housing space is actually more ample than your run space for your LF, proportionally.
Your bantam coop would be fine for 20 chickens. Your LF housing would most likely be fine for 37 chickens, but your run would be more suitable for 20 birds. So you would need to be sure that they WERE out free ranging daily, as that would be a LOT of birds in a fairly small outdoor space (if you were going for that many birds...lol).
Of course if you are in an area that gets winters, I'd err on the side of caution and go with a smaller amount of birds, because although mine spend almost no time in the coop now, winter time is another story. I like giving my birds more space than minimum recommendations.