Todd, do you know about the Rome2Rio Website? It’s not always perfect, but can give you a good idea of your options, including the fastest, cheapest, and “best” way to get from one place to another. Unfortunately, Sorrento, Lucca, and Munich aren’t just down the road from each other, and there aren’t fast, easy, or super-cheap direct flights.
Naples is the closest practical airport to Sorrento. Pisa is fairly close to Lucca, and has an airport. But flying from Naples to Pisa takes time. Then, you still have to get from Pisa to Lucca. Rome2Rio suggests that going by train from Sorrento to Lucca is your best option, for time and cost, but it will mean changing trains twice, and will take more than 6 hours, total. Driving yourself is supposedly faster (not including rest stops), but do you want to spend 5+ hours in a rental car, and have to turn it in at a different rental car office than where you picked it up?
Even Lucca to Munich isn’t completely straightforward, either. Apparently the best option is a train to Florence, then a flight from Florence to Munich.