Green River Soda started in 1919 during prohibition, when Schoenhofen Edelweiss Brewing Company in Chicago began bottling the non-alcoholic beverages. It a primarily midwestern soda, made now by WIT Beverage Company. If they sound familiar, they also produce the Jelly Belly line of sodas, Goose Island sodas, and a few other soda brands. The Green River recipe was actually bough by WIT in about 2010. Made in Wisconsin the soda is especially popular in Chicago, more so on St Patrick's day, when the city of Chicago turns the Chicago river green.
Green River River claims to be a "lime soda with just a hint of lemon". Smells citrusy when opened. Sure is green. Very pleasant flavor, and I'm not a big lime fan. I would say that yes, Green River is lime tasting. I don't get the lemon, but the lime is sure tasty. I'd buy and drink again.