Not related to launchbox but I had experienced the same issue with other apps at work. I have a laptop 1080p and a 900p monitor connected to it. Quip and Musicbee are the two apps that from time to time do the same, it looks like that "cut" on the window is at the size of the smaller screen resolution, that means that it only shows up on the 1080p, if the window is wider than 1600px or higher than 900px, if I make it smaller it renders ok.
Maybe it's not related, but it can help to find the issue.
Edit: I got curious and did some testing at work. I couldn't replicate that behavior but something similar.To the left is my 900p screen and to the right the 1080p with Launchbox maximized. If Launchbox launches? in the 1080p screen, it works as expected in both screen, but if it launches in the 900p when I maximize the window on the higher resolution screen, then the window present the "cut" to the right and at the bottom, and it even occupies the whole screen including the taskbar.