Lyon to Bayeaux

Hi!
Note that it is Bayeux, with only one A.
It is an 8-hour drive, so you do not have time for a scenic route unless you stay somewhere overnight. And even if the fastest route is theoretically via Paris, the route via Tours is much quieter and thus recommended.
For an overnight: Chenonceaux would be perfect, it would give you a chance to visit Chenonceau castle before you continue! If you've already been to Chenonceau, Bourges and Le Mans are two small cities with lovely medieval town centers.

I would also consider taking the train to Rouen. There is one direct train a day from Lyon taking 3:45, a bit late in the afternoon unfortunately, but you could spend the night in Rouen, briefly visit the town in the morning, and rent a car in the afternoon to continue to Bayeux (2 hours away).

I used to live a bit north of Lyon and recently bought a house in Normandie after many, many auto trips from Lyon to Normandie and Bretagne.

Balso's suggestion is a good one, but if you're fixed on driving the whole way, I can give some suggestions.

It's not the most interesting drive in France, but if you want a little scenery go north from Lyon on A6 to Villefranche-sur-Saône. Exit there and take highway D43 to the northwest toward Beaujeu. You'll go through some very scenic Beaujolais hill country with vineyards as far as the eye can see. I hear they sell wine in the area. Soft, easy-drinking red wine. But I'm not an expert at that sort of thing. At a roundabout north of Odenas you'll need to take the road toward Chauffailles and Beaujeu (D337). More scenic vineyards. D43 splits from D337 northwest of Beaujeu, so stick with D43.

D43 eventually joins with D987 to go to La Clayette. Go that way. Helpful hint: the locals don't pronounce La Clayette as Law Klay-Ette, No. It's Law Klett. Go figure. There's a pretty château by a lake on the edge of town that you'll drive by. From La Clayette take D985 north toward Charolles (source of the name for the famous Charolais beef cattle). Just past Charolles get on N79 west (soon to be A79, with tolls and everything). Go west until you can take N7 toward Moulins. Moulins has a pretty medieval central core and a surprisingly good art museum.

Take D953 west from Moulins to D951 and then take that west to Saint-Armand-Montrond. Take D300 west from Saint-Armand-Montrond to A71 and head north on A71 toward Bourges. Continue on A71 past Bourges and past Vierzon (as an American, I always see Verizon when I read Vierzon).

Just north of Vierzon head west on A85 toward Tours, which would be a good place for an overnight stay. When leaving Tours (which, not surprisingly, has towers) take A28 toward Le Mans. I've heard Le Mans is nice, but I've yet to stop there -- do some searching on the Internet or with guidebooks if you'd like to stop by. Take A28 out of Le Mans toward Alençon, past Sees, and just north of Sees you can take A88 toward Falaise and Caen. Around Falaise, A88 becomes N158. Falaise was the site of a very important battle between the Allied armies and the Germans, which decimated most of the German army in northwestern France. I'm sure there are some memorial sites and museums associated with that, but I haven't had the opportunity to look into it.

As you approach Caen, take the Périphérique Ouest (the western bypass) toward Cherbourg. That will help you avoid entering central Caen, unless you want to do that, and there's lots to see there if you do. Anyway, go west on the périphérique until you exit onto N13, which heads straight towards Bayeux. You'll have the pleasure of driving past the amusement park called "Festyland" on the west side of Caen just before hitting N13. Maybe it's just me, but when I read "Festyland" I hear in my mind's ear "Infestyland" which has a whole new meaning in our pandemic-affected world. I haven't had the pleasure of visiting the wonders of Festyland.

You can't miss Bayeux once you're on N13. And on the way, you'll have seen a lot of central France few tourists (and even some French folks) haven't seen.