Background: Software companies must balance fast value delivery with quality, a trade-off that can introduce technical debt and potentially waste developers' time. As software systems evolve, technical debt tends to increase. However, estimating its impact on lead time still requires more empirical and experimental evidence. Objective: We conduct an empirical study investigating whether technical debt impacts lead time in resolving Jira issues. Furthermore, our aim is to measure the extent to which variance in lead time is explainable by the technical debt. Method: We conducted an industrial case study to examine the relationship in six components, each of which was analyzed individually. Technical debt was measured using SonarQube and normalized with the component's size, while lead time to resolve Jira issues was collected directly from Jira. Results: We found a set of mixed results. Technical debt had a moderate positive impact on lead time in two components, while we did not see a meaningful impact on two others. A moderate negative impact was found in the remaining two components. Conclusion: The findings show that technical debt alone can not explain all the variance in lead time, which ranges from 5% up to 41% across components. So, there should be some other variables (e.g., size of the changes made, complexity, number of teams involved, component ownership) impacting lead time, or it might have a residual effect that might manifest later on. Further investigation into those confounding variables is essential.