I don't know for sure about the Gen 3. maybe call Viridian back and ask if the mounting foot print is the same as the Gen 2. If so, you are good to go.
I know you didn't ask about this, so please take it only as a alternate suggestion; the TLR7/8 will fit the HK45C with one of @mattfrey 's custom mounting keys. Again, only a suggestion, if you are sold on the Viridian I get it. I have a Gen 2 Viridian on my fullsize and like it, and I have not swapped the TLR8 I have for it.
food for thought... I'm a bit concerned about the proprietary rechargeable battery. but to be fair, I don't know much about it....