I just used a program called Spacedesk to connect my phone (it was a bit laggy but thats probably bad phone preformance, I have quite an old phone)
You install the app, than install driver on pc and your pc will see your phone as second monitor.
I just used it for the first time, so I dont know if it is a good option for you or if the app is cable of controlling Resolume.
What I can imagine is that the computer always has the driver running, which means as soon as you turn on the app in your phone you can connect with that pc, it may work with a pc without screen, but just do the presets with a normal monitor first.
It is able to display as an output for Resolume.
It is an extension of your monitors, or if its the only one it is your monitor.
I didnt get touch to work properly in resolume, but you can use mouse and keyboard to controller resolume with phone or tablet.