I'm going to quote myself from the Batoto comments section here, because oh my god, my mind is blown, and people need to know:
Holy shit, chapter 13 is actually a really good Japanese poetry joke? It took me a while to get it, but there are specific words and images that are associated with seasons in Japanese, called kigo, kind of like in classical western art where skulls can symbolise death and an hourglass can symbolise time, that kind of thing. Common kigo for summer include the summer sea, swimming, cicadas, and... lilies.
The idol girl doesn't get it because she's not particularly literary-minded, but the manager is exactly the sort of nerd who references kigo to make a dumb joke about lesbians, just like I was about to do. I feel so called out.