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This is a cartoon which is very class conscious. The visitors are shown as vey haughty and the butler is full of deference. Her ladyship doesn’t seem to be at all bothered by her status. Not doing her exercises in the privacy of her bedroom seems unlikely but it makes the drawing more complete. She certainly could do with some exercise.
There really was a Women’s League of Health and Beauty in the 1930s and it became quite fashionable at the time. By 1937 there were 166,000 members.
This is the sort of thing that was being portrayed at the time. The ship is sinking but the diners and the waiters are making no attempt to save themselves. It is very unlikely that such a thing would have occurred. It certainly didn’t happen on the Titanic.