Vlad I just did about 10 different searches using the steps above, and I only ran into one case where the search result didn't show up when using the lens (but did show without it). I'll keep testing as I continue to use Kagi, but here are the steps:
Enter in Kagi: WATCH: Tucker Carlson Torches U.S. Senate Candidate John Fetterman
A link to the article (https://www.dailywire.com/news/watch-tucker-carlson-torches-u-s-senate-candidate-john-fetterman) should be near the top.
Then apply a user-created Lens with these values for the setting "Include only these sites in results (up to 10, comma-separated)": wsj.com, dailywire.com, foxnews.com
The article won't appear in the search results using this lens.
Question: do search results using lenses take into account the ranking the user has given to a website? In my case, since I've ranked Daily Wire as "High", I think it would be reasonable to expect that I'll see results pointing to it when using a lens that includes this site. But even if that's the case, I understand there needs to be an underlying relevancy setting at the search engine level to deal with the case where all the websites in a lens have the same user-assigned ranking.
Separate thing that I noticed is that some of these results aren't actual articles; sometimes they're PDF documents, sitemaps, lists, etc. Unrelated to the issue this thread is for, but just an FYI in case that's useful to know.