I have planned this trip a few times. I have made this trip several times, but not in my Lucid. If you are not set on your route and go where the apps tell you, it should be easy, especially if you go through Atlanta (almost no other way) and then through Montgomery, AL, Mobile, AL and on to New Orleans. If you are going through Atlanta, Birmingham, Tuscaloosa and down through Mississippi, it is much more difficult. The trip is a LONG one-day trip and I almost would not do it in the Lucid as having to charge will make it that much longer. I would take it easy and plan for a two day trip with overnight charging at some point. You can do it in Auburn, AL or Montgomery, AL. There are quite a few places to choose from on that route. Auburn is almost exactly half way and I know of a couple hotels there with chargers. It is 370 miles from Charlotte to Auburn, so you should make it without stopping in Atlanta. I would charge at the Gulfport Outlets for as long as you can tolerate doing a little shopping just to make finding a place to charge in New Orleans a bit less stressful.
I have not found many chargers actually in New Orleans at all unless you can find and stay at a hotel that provides one. I am in New Orleans once a month. I will be there again in a couple weeks, back the first week in May. My in-laws live there, my son is at Tulane med school and we own a condo just off Magazine. BE VERY CAREFUL driving a Lucid in New Orleans. The roads are terrible, especially in the Garden District where the Oaks control the topography. Just walking down the sidewalk is treacherous. There are a couple chargers being installed down at Audubon Park and one at the Whole Foods, but most are at hotels, a few in parking decks.