Pete, there is no Save or Close feature after editing with Lightroom as folks have pointed out. What happens, is that Lightroom saves all the things that you do in what they call a "sidecar" file. If you look at the files using something like Windows Explorer (I don't know the Apple equivalent, but assume there is one), you will see a lot of files with the ending "xmp". For example, if you have a file called "File0987.CR2" (for Canon raw files), or "File0987.nef" (for Nikon raw files), then you should also have one called "File0987.xmp", assuming you have made some "Edit" changes. If you look at that file with a simple text editor (e.g., I have found that WordPad works best for me), then you will see how Lightroom stores the information showing the "edits" that you have made to your image. Lightroom doesn't really bake in the edits, like Photoshop does, until you do something with the image. For example, if you "Export" it as a jpeg, even if you only store the jpeg on your hard drive, then the edits are incorporated into the jpeg. If you attach the image to an e-mail, then the edits are applied to the image prior to Lightroom getting it ready for the e-mail. Also, if you Print the image to a printer, then Lightroom makes all the changes that you did in the edit before sending the "product" to the Printer.
If you want to see this, open Lightroom, select an image that you know you have edited and then go the Edit module. On the left side of the screen, you should be able to find a top level item that says "History". If you click on the little arrow that is beside the word, so it is pointing down, then you will see a listing of all the "changes" that you have made to the original image. What is being displayed here, by Lightroom, are the contents of the "sidecar" file, the one that ends with "xmp". The fact that Lightroom uses this "xmp" file, is why you can back out any of the changes that you made, or keep "snapshots" of your images during the development process and produce multiple copies of the same file with different "develop" processes attached to them. For example, when you make a "Virtual copy" of an image, Lightroom does not really make another copy, rather it keeps track of all this "activity" in the xmp file. This also is why you should backup your Catalog after every edit. I have my LR set up to prompt me to back up the Catalog after each editing session, something I always do. Mind you, if I have just opened up LR to check on an image with no editing, then I won't backup the Catalog.
This is why it is also a good idea to backup the Catalog as well, every time you backup up your image files. That way if something happens, then at least you have a catalog that matches the backed up images.
I hope this explanation helps you to understand why Lightroom doesn't "Close" or "Save" a file. Any questions, post back and I will do my best to answer them.