I've got LR5 (with the updates) and run it with Windows 7. I lost the LR5 icon and the program does not show up in the "All Programs" menu on the Start button. However, it does show up in the "Programs and Features" section in the Control Panel. Some how I was able to get LR5 to associate with a generic Icon on the desktop but I have to install it every time I launch it. How can I get back to my LR5 icon and have it launch and pick up where I left off when I last closed the program instead of having to install it every time I use it?
You should be able to find Lightroom.exe in folder- C:\Program Files\Adobe\Adobe Photoshop Lightroom 5.6
Right-click mouse on "Lightroom.exe" select "Create a Shortcut". It will suggest you place it on your desktop.
This shortcut icon can be dragged onto the 'Quick Launch' bar of Windows, also right-click the icon to "Pin to Start Menu"
When updates are installed the 'old' [Lr] icons are changed to look like a blank page - these can be deleted. The update should have created 'new' [Lr] icons.
It is also possible to create shortcut icons for specific catalogs (if you have more than one)- R-click on the Catalog.lrcat file to achieve this.