I helped public healthcare officials implement balanced score in the past. Here is one source that may help you; http://www.balancedscorecard.org/BSC-Basics/About-the-Balanced-Scorecard
You may refer to the following article which show the integration between lean management and six sigma: Edward D. Arnheiter, John Maleyeff, (2005) "The integration of lean management and Six Sigma", The TQM Magazine, Vol. 17 Issue: 1, pp.5-18
If your research includes the public and voluntary sectors, the following two publications might be of use:
Moullin, M. (2017) Improving and evaluating performance with the public sector scorecard, International Journal of Productivity and Performance Management, Vol. 66 Issue: 4, pp.442-458.
Moullin, M. (2009) Lean and Six Sigma – Can they really be applied to the public sector? Public Sector Executive, May / June 2009.
Links to these articles are available at www.publicsectorscorecard.co.uk
Suggest that you check out the article "Positive Metrics Poor Business Performance: How does this Happen? https://www.smartersolutions.com/orl/Positive-Metric-Performance-Poor-Business-Performance-LINKS.pdf
Let me know if you would like to discuss application of the next generation operational excellence and balanced scorecard methodology.