How to get from Air BNB to early train/airport departure?

I suggest asking your AirBnB hosts as well.

As to getting from Old Town to the airport, I recommend Friend in France https://www.friend-in-france.com/. They offer a private transfer that at 35€ costs just 3€ more than the flat rate taxis and they are very good. I don't think the buses are running that early so your options are a private car service like Friend in France, an Uber, or a taxi. I have no idea if Ubers are generally available that early in Nice but if they are and there is no surge pricing, Ubers should be around 20€

Ask your hosts to book a taxi for you.

In Lyon, I was happy using Lyon Taxi Prestige. You can phone or email. If you have your train ticket, there’s no reason to arrive at the station more than 10 minutes before scheduled departure. And remember there are 2 railway stations in Lyon so make sure you know which one you need.

....Our flight home leaves from Nice at 6:30 AM...this means we would need to be at the airport in Nice around 4 AM........ Are you sure? Most likely the Nice flight is domestic flight connecting to your flight home so 5 or even 5.30 should plenty of time especially that early.

Frank, it is a train at 6:30 am not a flight.

Norma, how or when does ---- Our **flight home leaves from Nice at 6:30 AM** --- become a train?????

Ohhh! I was reading the line “Our train from Lyon-Nice leaves at 6:30 am.”

The post says both. The OP needs to proof this and correct it.

There are two 6:30 am departures. One in Lyon to the train station and one in Nice to the airport. It is clear to me.

Yes, the post is quite clear on timing. There is a 6:30 AM departure on a train to Nice. Then, after staying in Nice for however long, the OP is leaving on a 6:30 AM flight. The only typo I see is the "-" between Lyon and Nice. It would have been more clear if it had been replaced with "to."