Many photo web sites are designed so that visitors aren't encouraged to save copies of photos, and there's no particular reason why LrWeb should be an exception and have a "download link". What task are you really trying to accomplish?
Anyway, you can save an image through your browser, though this varies between browsers. In Firefox, right click the image, choose File Info, then the Media tab.
Does what you said actually work in Firefox? I have tried right-click in both IE and Chrome and no image is recognized, only an HTML page. To get to the image URL I have to do an Inspect Element then poke around in a DIV a few up from where Inspect Element lands, and copy a relative URL from an IMG tag then paste that into a new browser tab with the proper hostname in front, and then the JPG image opens in that tab, and I can right-click save it.
I imagine saving an image from lightroom.adobe.com is supposed to be almost impossible. The images displayed are not JPGs that have been exported from LR at a certain size and sharpness and watermark like a normal web-gallery might contain, they are whatever the website coding derives from the smart previews (of adjusted raw files in my case) that have been synced to the cloud and could change on a daily basis at the whim of whatever Adobe decides they want to do with this website and since there is no way to watermark the images, I expect Adobe is hoping that clients can't save images from the website if you give them a limited-viewing URL.