Hi aimeelouisebarr,
Unfortunately there is not a way to use a remote like the RC-6 while the camera is also set for tethered shooting. It can only use one or the other. When you are tethered shooting you will either need to use the shutter button in the software or the shutter button on the camera to take a photo.
Through Canon support we only have information on Canon products, so we do not have information on the tether shooting features in Lightroom. If you want to use our EOS Utility software to tether shoot there is a timer controlled shooting option. That would add a delay between when the shutter is pressed and when the photo is taken. That way you have more time to pose in the frame before the photo is snapped.
If you want to use our software it is available HERE. Once you are on the web page click on the Software & Drivers button and the current version is EOS Utility 3.16.11. The steps to use the time controlled shooting function are listed HERE.
