With webstart, you can save your data on the PC. You have to sign your application for this, but you have to do that anyway when using LWJGL.
About Eclipse, there is no compiled jar...just the classes, usually in the bin-directory. If you want to make it a jar, you can do so in Eclipse somewhere, but it's pretty awkward IMHO. What i usually do, is much simpler: Install 7zip (or similar), zip the content of the bin directory, rename the file to .jar...done.