Sustainable finance has emerged as a vital tool in addressing global challenges related to climate change by directing capital towards ventures that promote long-term environmental and social sustainability while also generating financial returns. Banks, being a cornerstone of financial stability in any economy, play a pivotal role in this context. By integrating sustainability factors into their practices, banks can create positive ripple effects across various economic sectors due to their significant influence on resource allocation. However, to encourage lending towards greener assets, banks need appropriate incentives. This study aims to explore the relevance of bank lending (carbon-neutral versus carbon-intensive) on its sustainable performance and the impact of internal supervisory channels, such as board characteristics and financial innovation, in shaping such lending behavior. While credit risk is a crucial element in the lending process, sustainable finance necessitates that banks consider borrowers' environmental, social, and governance (ESG) aspects in addition to traditional credit metrics. Thus, by integrating non-financial factors with traditional credit risk metrics, the present study seeks to construct a sustainable financing framework that allows the identification of responsible borrowers while controlling for the risk of default and ensuring returns. This approach promotes better resource allocation and reduces the risk of adverse selection through responsible banking practices. To achieve its objectives, this research will employ a mix of quantitative methods, including panel data regression analysis and Autoregressive Distributed Lag (ARDL), and qualitative methods such as the Fuzzy Delphi Method, Fuzzy-Analytical Hierarchy Process (AHP), and consistency tests. This comprehensive approach will aid banks and financial institutions adopt responsible behaviors across all operations and support policymakers and regulators in incentivizing sustainable practices for a green transition.