I looked at the manual and more specifically at the Part/Controls section and did not see a lens cover. The manual does state that the camcorder automatically turns on when you open the LCD viewfinder. There are a couple of things you can do to protect the lens one of which is to get a lens cap that would fit over the lens (52 mm lens cap).
A lens cap can be purchased for under $10 and you can get one that comes with a strap to attach it to the lens barrel so you don't lose it.
I would recommend a UV filter to protect the lens against scratches when you are recording. A UV filter can also be purchased for under $10.