This is a longtime River3 feature request, and I finally got some time to work on it this week.
There's a little work involved in setting it up, it involves understanding how JSON works (or some careful and intelligent guesswork). It's not for the faint of heart.
1. To turn the feature on, bring the OPML Editor to the front, then bring river3data.root to the front. Navigate to river3Data.prefs.flBuildTabbedRivers and set it true.
2. After the next scan you'll see a new file in the misc folder, riversAuto.json. Copy it into the new tabbedRivers folder, and rename it to rivers.json.
3. Open it in a text editor. You'll see that it's a list that has one element for each of your lists. Only the url and title attributes are set for each item (because that's all the info River3 has). You can fill in a longTitle and description, and if those are non-empty, they will be displayed in the title bar of the river when its tab is active.
4. Save the file when you're done editing. It will be read the next time River3 does a scan and the river will be generated with the new values.
5. Be very careful with the punctuation in the JSON. Even the slightest error will cause the tabbed river file not to work. You're doing a little programming here.
This is what my tabbed river looks like after I edited the rivers.json file.