AFAIK gender balance quotas are no longer in effect.

Gender ratios are widely tracked within the industry, though, e.g. (https://ylw.yale.edu/top-firms/). Also clients for legal services often have their own diversity requirements (https://www.nytimes.com/2017/04/02/business/dealbook/faceboo...).

If you're looking for a historical reference, (https://scholarship.law.cornell.edu/cgi/viewcontent.cgi?arti...) is 26 pages and covers the history of women in law from 1920 to 1970. Cynthia Epstein's Women in Law should cover this topic but I haven't yet read it.