What Chris said is correct, you can just update the license to upgrade your Essentials installation to Professional, but that wouldn't switch web servers. 

One option is to install Forms on the new web server, license it using the Professional license, then point it to the same database as the previous Forms server. This would keep everything you had previously, processes, history, forms, teams...

If you install Forms on the new server and point it to a new database, you can bring the process XMLs over which include the CSS, JS, field rules and access rights**, but it wouldn't include all of your instance history and in in-progress instances. It would just bring the definitions over to start from scratch. You'd also want to bring your teams and other resources over as well. Unless you are looking for somewhat of a reset, I recommend the first or second option of using the same installation or using the same database. 

** Access rights would only carry over if the users are mapped. Since you are upgrading from using repository authentication to LFDS authentication, you'll want to run the Forms user migration tool to switch your users from the repository users to their LFDS counterparts. 

In this circumstance, you are changing a lot of things. I'd recommend first updating your existing Forms to work with the new LFDS system, by swapping the license, changing authentication methods and running the user migration tool to get all the users set up. Once the existing Forms is all set up with a Professional license and LFDS, you can more easily install Forms on the newer web server and point it to the same database that's already set up.