I have my Roku Premiere connected to a HDMI audio splitter. The HDMI output from the splitter goes to the TV.
When I am using the Roku Media Player channel to play music, from a DLNA source, I only need the TV on to view the Roku menus. Is it possible for me to view, and control, the Roku menus from a mobile or laptop so I don't need the TV on?
I know the App will allow me to control the Roku but, unless I've missed something, it won't allow me to view the Roku's display?
If you used plex instead of dlna as the player you could do it - sort of anyway. The plex app on a phone/tablet/pc can act as a controller to any other player although you have to have started plex on the roku before it will show up in the player list.
So, you'd have to use the roku phone app to power the device on, pick plex from the 'recent channels' you see at the bottom of the remote control screen (and I think you have to hit the OK button at that point to make it start. Then with plex started on the roku, just use it on any other device like your phone to pick the album/playlist you want and use the roku as the player. Emby might do that too, I haven't tried it for a long time.
If you want to make it more complicated, Alexa has skills for both rokus and plex so in theory you could ask an Alexa device (or app on your phone) to ask plex to play something on the roku. I haven't gone that route because it requires your plex server to be set up for remote access to work. (Just checked and it does work to say 'start plex on the roku' to get to the point where plex is running, though).
I'm not really sure a roku will output anything if it doesn't have the HDCP handshake from your display, though.