The proliferation of large language models (LLMs) has revolutionized the capabilities of natural language interfaces (NLIs) for data analysis. LLMs can perform multi-step and complex reasoning to generate data insights based on users' analytic intents. However, these insights often entangle with an abundance of contexts in analytic conversations such as code, visualizations, and natural language explanations. This hinders efficient recording, organization, and navigation of insights within the current chat-based LLM interfaces. In this paper, we first conduct a formative study with eight data analysts to understand their general workflow and pain points of insight management during LLM-powered data analysis. Accordingly, we introduce InsightLens, an interactive system to overcome such challenges. Built upon an LLM-agent-based framework that automates insight recording and organization along with the analysis process, InsightLens visualizes the complex conversational contexts from multiple aspects to facilitate insight navigation. A user study with twelve data analysts demonstrates the effectiveness of InsightLens, showing that it significantly reduces users' manual and cognitive effort without disrupting their conversational data analysis workflow, leading to a more efficient analysis experience.
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