Well, it used like many times, so I would say simile. However, an analogy can use like or as to, so I'm not too sure. But, I'm going with simile.
What really happened was that Algernon ate the sandwiches but probably would make Lady Bracknell, so, when she asks about the sandwiches Lane says that there were no cucumbers available in the market.
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Write about a good experience you've had recently and how that experience was special to you, include a message in it. Half a page to a page should do. After you're done looking over it, make that message in your story that you want to convey the theme and the reasons behind it. I can't write this for you since I don't know who you are, but you know who you are.