If you were skittish about calling an amalgamation of legumes and oil “burgers,” courtesy of Beyond Meat, you definitely aren’t ready for what’s next. Finless bluefin tuna—that is, tuna made without the use of a once-live fish— could be coming soon to a grocery store near you.

While vegetarian innovations have taken center stage recently in “food tech,” another alternative to butchering or farming actual wildlife is on the rise. Lab-based meat startups are racking up millions of dollars to grow it. Bay Area-based Finless Foods...