Sorry, I don't have an RX1 but for a possible money-saving idea, if you bought the camera with a credit card, check if that credit card offers a free extended warranty benefit. Almost all of my credit cards have this free benefit -- usually extending the manufacturer's warranty by up to 1 extra year.
This benefit has saved me thousands of dollars over the years when something needed repair, usually right after the manufacturer's warranty has expired! In one case a few years ago a Samsung LCD TV panel failed about 2 months after the original warranty expired and the repair would have cost over $2K USD. I sent in a repair estimate and got a check for the full amount about 3 weeks later.
The RX1 firmware already allows two options for turning the LCD on and off whenever you want. One option is to set "Finder/LCD Setting" to manual and use the button on the side of the EVF. The other option is to assign "Deactivate the LCD" to one of the programmable buttons.