To me, the theme of this story is that it is best for people to be content with what they have and not to start dreaming of things that (they think) will be much better than what they have.
The couple in this story were relatively happy with one another. But then they thought they had won the lottery. Once they thought this, the husband especially began to have big dreams. He became dissatisfied with what a moment before had been an acceptable life.
Another way you could look at it is to say that the theme is that you should not let a change in your wealth (or other circumstances) change who you are as a person.
I'd say the theme of "The Lottery" by Anton Chekhov is that your outlook on life in general, and on your situation in particular, is based on the possibilities open to you. Those possibilities, of course, are based on your employment, your financial situation, etc. Once you've adjusted yourself to your particular niche in life, you find your happiness and contentment in that situation. But if a different, perhaps better, possibility opens up, or there's even a hint that such a possibility may come open, you begin thinking of newer things that might now be available to you. The problem is, if the possibility does not materialize, you are left with a bitter taste in your mouth.
Full elaboration in my article at link provided.