The Panasonic Lumix DMC-GH4 was first supported in Lightroom 5.5.
Unfortunately, support is never retrospectively added to older versions so you're faced with two choices:
Thanks so much. What would be the easiest.
Well, upgrading to Lightroom 5 costs money but gives you better software and a simpler workflow.
Using the DNG converter is free but means you have to convert every single Raw photo to DNG every time you shoot before you can edit the photo in Lightroom 4. Awkward workflow for some. Others don't care and prefer the free route.
Your choice really.