Hallo nixpixstix,
If you are satisfied with the profile you can get via entering the Make "Sony", you have an option to set this as your default for all .ARW-files from Sony RX100.
Proceed like this:
Select an image from a fresh import and go to Develop module. Make sure that no setting is changed, unless you always deliberately want it as a starting point (e.g. in Camera Calibration Panel "Camera Standard rather than "Adobe standard").
Go to the Lens Correction panel and manually set the Make "Sony" and the Lens profile you like best from the available choice.
Then go to the Menu "Develop - Set Default Settings..." and choose "Update to Current Settings".
In case you have your defaults per ISO (rather than to specific per camera serial no. or not even this) you need to repeat this for each ISO.
This enforces that all your Sony RX100 ARW-files will get this Lens Correction applied.
Cornelia