Only problem is there is no requirement to be an attorney in order to be a justice on the U.S. Supreme Court.
But falsifying reports or ethics violations might be grounds for ineligibility as a SCOTUS Justice.
No, there isn't a requirement. However, as she is an attorney [and knows the law against falsifying evidence], if she were sanctioned by SCOTUS - her nomination might be in peril.
I did hear of this allegation about a month or so ago - where some commission or organization produced an opinion on partial birth abortion in a dociment. Kagan then wrote a paper for the Clinton Administration that significantly departed from what the opinion stated. That paper was then submitted to SCOTUS during a subsequent case.
Her writing the paper did not in and of itself constitute a vioaltion - as long as she [herself] had no involvement in its submission to SCOTUS. However, if she was the one who submitted it to SCOTUS [or had knowledge thereof of its submission], and did not notify SCOTUS of its inaccuracies - she might have a problem.