Answer: you can install the lens cap, the same diameter can be 

hi,please choose 67mm lens cap. 

The Answer is Yes. You can use a pinch cap over most filters. ALL my lenses have a filter of some sort on them. I use to use a lot of "traditional" lens caps on all my old Nikkor lenses but putting them on and taking them off became a giant PITA, so I got a Pinch Cap as a test. I then converted ALL the lenses to Pinch Caps. Hope this helps. 

The V50x comes with a skeleton case with a slotted rear door replacement, but there is no opening to allow plugging in an external mic. As a note, the sound recording, even while in the completely waterproof case, is better than I had expected. If you're not worried about moisture, there is a threaded tripod mount on the bottom of the camera and an adapter that will allow you mount the camera without using the case. 

Same caliber can be installed the lens cap