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lucy24 - 9:56 pm on Nov 6, 2012 (gmt 0)
RewriteCond %{REQUEST_URI} /Landingpage/index\.html$ (tried with this)
REQUEST_URI is not the page that "owns" the image; it's the image itself. Each request is an island. In fact I've got a strong impression that several previous people in this thread have pointed out that you don't need to say anything about REQUEST_URI at all, since that's going to be in the body of the Rule.
Unless -- further horrid thought -- you use the same background image on more than one page, but you only want to rewrite it in one place? If so, that's where you would need a Referer line. It would be your own page-- or your own stylesheet, if it's a separate file-- not the visitor's previous location. But then you're back to the question of UAs that don't send a referer. (Or is that what the REMOTE_ADDR option does? Someone else will know.)