Hi bootareen, welcome to the forums!
Source is often where you can find the library's component parts in separate files, if you're intending to work on the library itself. Lib will often contain dependencies that are necessary for the main script to run such as jQuery, or that are included for demo purposes. Dist will normally have the main file that you want.
It shouldn't be a problem in most cases, as usually JS files don't include other JS files or CSS files directly.. you have to reference them in your HTML files. The only thing you'll want to keep an eye out for is the order in which the files are loaded.. you almost always want to be loading jQuery first, for example.
I guess it's a matter of personal preference.. as long as you adopt some kind of folder structure as your project grows, and stick to it, it should help to keep things manageable. I usually create a subfolder under my js folder called libs where I keep jQuery and any plugins etc.. and my own code goes directly in js (and subfolders where necessary).