Technical Debt Management (TDM) includes activities such as identifying, measuring, and prioritizing technical debt. It is mainly performed to proactively mitigate the risk of losing the maintainability and evolvability of the software product which results in reducing the team velocity. Despite the importance of TDM, its adoption in software companies remain limited. Soft-ware companies are witnessing high market demand and competition that make delivering customer value outweighs the effort invested in TDM activities. Since the impacts of technical debt are uncertain and evident only in the long run, it is more difficult for companies with very limited resources to proactively spend their resources on TDM. In this paper, we propose a lean approach to facilitate the adoption of TDM in software companies with very limited resources. Based on this approach, TDM is driven by project management metrics, such as team or sprint velocity, and velocity variance. We conducted an initial evaluation of the core concept of this approach through a short survey of 43 software project/product managers. Most of the survey respondents have a positive impression about our approach, which will encourage us to proceed further using more robust empirical evaluation.