I also have this problem with my LG Urbane watch, which I reset over the weekend because it was being very slow and I hadn't reset it in many months.
I am finding that the messages are not coming to the watch, although my other messaging apps are working fine, including Gmail.
When I type in Verizon message in the Play search bar on the watch itself, it shows the app but it says it's not compatible with this version of android wear. Which is weird because I had it just two days before, and my watch says it's updated to the latest version of android wear.
I have an Lg V10 for my phone, never had problems with the messages coming to my watch til now.
I was not having any issues with the app on the watch before the reset. I don't usually use it to dictate and send, but I could always read and ignore messages from the watch.