Do I need a car in cote d'azur? Also help with the itenerary.

That's a very packed itinerary. I assume you will be taking a train to Lyon and then onward to Avignon. I assume you are going in early to mid July, but a car or tour would be required to see the fields. Which fields matter in the time frame you are going -- the later in the season the higher you must go. You can rent a car from Avignon and drive through the Luberon or the Valensole plateau and continue on to Nice.

In Nice, in early July, a car can be very challenging. A car is primarily useful for getting to the countryside/backcountry or to Eze, if the bus is too full. Even then, it might just be better to take an Uber to Eze and then a taxi or Uber back down to Villefranche sur Mer. There have been days in July (typically, on cruise docking days) where you are forbidden to drive into Villefrance-sur-Mer and need to park at the upper road/garages, and walk the steps down and up (vs. the train, which is at sea level).

Getting to Cannes by train is easier than driving. The train stops literally in the center of the town, a few blocks from the beach.

Bring up a google map of the sites you want to visit and do a linear tour between overnights to give you a better idea of distances and time needed. A car could be a convenience, but you will often find that you will have to park in off-site lots and still have a bit of a walk. I personally can't get excited about the lavender, since it grows in my yard, but it might make sense for you to go on a tour and be sure to include the Perfumeries near those fields. Avignon is a good stop to see the Pope's Palace. Aix-en-Provence is quite busy.
Arles is smaller and has a Roman Arena and has the Ghost of Vincent Van Gogh. Nice has a wonderful Old Town with a Flower Market and the Chagall Museum. The Beach in Nice is mostly controlled by the Hotels and you pay for chairs, etc. You can take a commuter train along the beach towns. Make sure everyone has shoes that can walk on cobble and is safe on climbing up or down marble or rock steps. Bon Voyage!

I am a bit confused about your route. Are you going from Paris to Nice, then back to Lyon and/or Provence? It sounds like you are back tracking, but maybe after Nice you are heading back to Paris for your flight home. As Kathleen says, take a look at a full map to orient yourself, pinpoint your must-sees, and route yourself accordingly. I think of Lyon, Avignon, etc. as stops along the way between the Riviera (Nice) and Paris. The Riviera is the southeastern most part of Provence; Avignon is on the far west of Provence; Lyon is about 230 km north of Avignon. You may have other ideas about your route, of course.
As for a car, we like to have one in Provence (which, by the way, is a large area of over 12,000 square miles). On the Cote d'Azure I think the parking situation makes a car disadvantageous. Trains and buses between towns are very convenient there. As to transport between the town you choose in Provence, and Nice, I would opt for the train to avoid the problems driving and parking in Nice. Having a car in Provence is helpful for exploring the area. Lavender viewing is a variable, depending on location and weather. There are usually no guarantees.
Definitely look at a map of France to see what we are talking about. It should help you decide.
Bonne chance!

P.S. Be sure to factor in the amount of time to go from Nice to, say, Avignon or Aix-en-Provence, whether taking a train or driving. If driving, the site viamichelin.com gives good route options and times, but add in an hour or so to account for gas/food/comfort stops.
If taking the train, check routes and schedules on sncf.com, the official French train website.
This applies to the reverse route, of course.

I am going to Nice from Paris via an overnight train. We are going to Chamonix and then to Switzerland via Geneva after Lyon. This is why we are going to Nice first and then to Lyon. We will be in Nice on June 25th and June 26th.

Thanks for the clarification.

If by chance you rent a car for Avignon/Lyon areas, be sure to return it in France, not Switzerland. There are humongous fees to drop off a car in a different country, in the 500-1000 euro range.

Thank you for the clarification. You can pick up your car on the way out to the countryside, then. You can journey to the airport and the car rental locations are near garage P5 (easily reached by the tram stop for Terminal 2). You can then easily get on the autoroute to head to western Provence.

And yes, you will want to return your car on the French side of the Geneva airport, near Meyrins. Remember that a vignette (and Stick'Air in Geneva) are required.