Background: Software companies must balance fast delivery and quality, a trade-off that often introduces technical debt and wastes developer's time. Technical debt tends to increase as software evolves, which is assumed to slow down development and maintenance activities. However, the potential relationship between technical debt and lead time lacks empirical evidence.

Objective: This paper reports an empirical study to explore the potential relationship between technical debt and lead time in resolving Jira tickets. We further aim to measure the extent to which technical debt can explain the variation in lead time.

Method: We conducted an industrial case study to explore this relationship in six components, each of which was analyzed individually. Technical debt was measured using SonarQube and normalized with the component's size. Lead times to resolve Jira tickets were collected from Jira and averaged monthly.

Results: The study found little to no correlation between technical debt and lead time to resolve Jira tickets in five components, with technical debt explaining a variation in lead time ranging from 0% to 41%. However, it is less than 30% in most of the components.

Conclusion: Technical debt alone does not fully explain the variation in lead time. There should be some other confounding variables (e.g., size and complexity of the changes, number of teams involved, priorities, component ownership) affecting lead time or a residual effect, i.e., interest, that might manifest later. Further investigation into those confounding variables is essential.