Of the two, I much prefer Lottie for a full name. There’s always a lot of angst about how children must have a formal name, and while that would be my preference, there’s nothing objectively wrong with a diminutive as a full name. At the last ONS name release Rosie, Elsie, Evie, Millie, Maisie, Hallie, Lottie, Molly, Ellie, Gracie, Harry, Archie, Freddie, Charlie, Alfie, Tommy, Teddy, Albie, Reggie, Ronnie, Frankie and Bobby were all in the top hundred. These names are totally normal and will work for adults because there will be thousands of adults with this style of name when your Lottie is an adult.
She might end up disliking the informality of Lottie, or if you called her Charlotte she might wish you’d just called her Lottie as that’s all she’s known as. There’s nothing to stop a Lottie going by Charlotte professionally if she wants to. There’s no way to know how she’ll feel as an adult, and as Charlotte and Lottie are both very popular, either is probably fine. And if she really hates her name, it’s free and easy to change as an adult.