When a customer puts a product into their cart, it places stock of that product in reserve so that another customer can't also purchase the same unit of stock. This doesn't do much if you have lots of stock but if you're down to your last one of something, it will help prevent the unfortunate situation in which two customers placed an order for something that you only have one of.
The missing step is when the Order in Lightspeed is dealt with in some way, it needs to be reported back to the Web Store so that the stock can either be reduced or removed. In order to do this, you need to enable the uploading of Orders in Lightspeed.
Simply go to the eCommerce window under the Tools menu and click on the 'Documents' tab. Here, you'll see check boxes for all the different document types. I check them all off but the most important is the one that says 'Upload Orders'. Check this off, save, and upload to your Web Store again to see if your products show up again.