I think I understand. You made a rubric in Canvas and you're trying to attach it to an assignment made with the Google LTI.
I don't think there is a way to use the Canvas rubric with an external tool, (which the LTI is). When you use the Google LTI 1.3 you are going to grade the work with Google even though you are in Canvas.
If students have already started working on the assignment, you can still edit the assignment to remake your rubric in Google.
If they haven't started the assignment yet and you'd like to grade the assignment with the Canvas rubric, then you can remake the assignment without the LTI (you can use a URL hack to force a copy of your Google document) and then you'll grade it in the regular Canvas speedgrader.
If
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