I feel like Lannes is one of the few men that Napoleon would listen to in any situation. Napoleon was often pigheaded and refused to listen to his subordinates, but it seems to me that if Lannes suggested something or reported something Nappy is quick to agree or comes running.
IIRC during the battle of Jena, Lannes left wing V Corps made first contact with the Prussian rear guard, reported it, and Nappy came running with the rest of the army as they then proceeded to beat down the poor outnumbered Prussians. Davout III Corps then had to face 1v2 odds at Auerstadt against the Prussian main body. Luckily for the French, Davout skillwise was equal to Nappy and he pulled off a win despite the odds.
If for example Davout and Lannes corps positions were swapped, and Davout reported 1st contact, i rather doubt Nappy woulda come running with the whole army. I've a distinct feeling Napoleon woulda been more cautious with Lannes all strung out on the march far away from the main body unsupported. Hell in that situation, i can see Bernadotte I Corps not being a dawdling bitch and come rushing to Lannes corps aid. Davout was a hard-ass liked by few and not a charismatic favorite like Lannes. If Lannes got killed or wounded due to Bernadotte's dawdling, Nappy woulda legit shot his ass for negligence or at the very least strip Bernadotte's rank and boot him. If Bernadotte quickly supported Lannes at Auerstadt and helped score a major victory then maybe there wouldnt be a rift between Nappy/Bernadotte and he wouldnt have gone off to Sweden.
Lannes was one of Nappy's best men and fiercely loyal, so if he survived the long haul, good odds he'd get killed after Nappy's 1st abdication. If he still managed to survive that and was preset at alt-Waterloo (or taken Davout's place in Paris and Davout goes to Waterloo), Lannes surviving would prolly help Nappy drag out the inevitable a bit longer.
Would be interesting to see the butterflies if Wellington-Blucher were crushed and the Russo-Austrians had to finish the job.