Agile methodologies are employed by software development teams for collaboration and adapting to changing requirements. However, this flexibility may lead to technical debt (TD), causing potential bugs in the long term. Lean principles, focusing on waste elimination and continuous process improvement, can be applied to manage TD in agile software development. This research conducts a systematic literature review on using lean and agile methodologies for TD management. The review identifies 34 papers, categorizing TD types, pinpointing lean and agile principles, and aligning technical debt categories with suitable lean and agile principles. Additionally, three existing technical debt management frameworks are identified: the TAP framework, the LTD framework, and the CoDVA framework. The study concludes that integrating lean principles into agile software development assists organizations in effectively managing technical debt. Furthermore, the research offers insights into selecting the most suitable TD management framework based on an organization's needs and available resources.