To use a YARA rule from a private Gihub repository you will need to make use of an Authenticated Resource Locator.
Create a token in Github
In Github go to Settings and click Developer settings in the left hand side bar.
Next click Personal access token followed by Generate new token. Select repo permissions and finally Generate token.
Connect LimaCharlie to your Github
Inside if LimaCharlie click on YARA Scanners in the left hand menu. Then click Add YARA Source.
Give your rule collection a name and then use the token you generated with the following format linked to your repo.