The remote is a Y04G0051 and with some googling, I found a lot of pages that link to supposedly working configurations, which on closer inspection all apply to slightly different model numbers. Virtually none of these supposedly working configurations actually makes use of all buttons on this particular remote. For instance, most do not have mappings for the Vol± and Ch± buttons and instead use the blue arrow buttons for this.
That's somewhat annoying, so I did some additional searching and then combined the various results into a set of configuration files that work.
Attached are the four files you need to make this remote work with MythTV. I hope this means you don't need to spend a day searching for and combining config files, like I had to.
This file contains an udev rule that makes the remote's entry in /dev/input persist across reboots, by creating a symbolic link to the correct /dev/input/eventX file. It goes into /etc/udev/rules.d.
This file tells the LiRC daemon which driver and which device file to use. It lives in /etc/lirc.
This file contains the mappings from keypresses on the remote control to configurable events. It also lives in /etc/lirc.
This file links the events defined in lircd.conf to actual keypresses for applications. You can edit this file to change mappings or to add applications. Don't change any of the other files, though. You can save this file as .lircrc in the home directory of the mythtv user.