I've driven all of these routes in my Model S and most of the routes I have driven many times over the years in ICE vehicles as well.
If you have never been to Death Valley, I would take the route through the National Park. Since you're just doing a drive through, I would try to see the Furnace Creek Visitor Center, Badwater Basin and Zabriskie Point. They are all fairly close to each other and you will see much of the rest of the park on your drive through. Taking the direct route from Las Vegas to the Lone Pine supercharger and seeing all three of these places on a single charge would be really tight even in a LR Model 3, but it could be possible given the warm weather if you drive slowly. Another possibility is to just stop and top off at one of the L2 chargers mentioned previously in this thread.
If you want to play it safe, rather than taking the direct route from LV to Lone Pine, you could drive LV to Beatty first and top off at the supercharger there and then drop down into the national park and see those 3 places I mentioned before heading east to Lone Pine. This is not very direct and will add over an hour to your trip. You will also mention the aforementioned Amargosa Opera House by going this way and that is kind of a cool place.
The middle route is the most boring imo although that Deep Springs College that cpa mentioned does fascinate me. I don't think you can stop and get a tour there or anything though so not really worth making that drive.
The northern route takes you up into high elevations near the CA/NV border and is quite scenic. Snow can be a real issue on that drive through much of the year, but in September it should not be a problem.
Believe it or not, a couple Aprils ago, I drove through Death Valley and it was 100F and as I left the park around sunset, I noticed a storm coming in and even felt a few rain drops. Then I ended up on this northern route and hit snow a few hours later near the CA/NV border and hit heavy snow as I approached Mammoth Lakes. The last few miles of driving into Mammoth was ill-advised with all-season tires in that weather, but I was too low on charge to turn south and head to Lone Pine. I was lucky to not only make it to the Mammoth supercharger without getting stuck in the snow, but also to be able to find a room within walking distance of the supercharger, so I plugged in and walked to the hotel (This was before idle fees and the supercharger was never going to get anywhere near full anyway). When I woke up my car was buried in about 2 feet of snow at the supercharger lol. I waited till just before sunset that day to drive out of town and fortunately the roads to the south had been cleared so I made it out that way (I was headed north so this was a huge detour, but I was just happy to get back to dry land

).