There are two possibilities, your LLL is actually slowing down, or the websites are getting heavier.
I could imaging your internal flash is worn-out (how old is it? 4 years? 5?) causing the disk cache of the browser to slowdown the whole user experience.
But of course websites aren't getting any leaner either. And an LLL is not really equipped to handle lots of javascript. If you haven't done already you could install 3MX, and use the Dillo webbrowser, which doesn't support javascript, and just ignores it. Unfortunately a lot of sites just won't work without javascript.
Sorry, Puppy won't run on your LLL. Puppy is x86 only, and your LLL has a Mips processor.