Truthfulness (adherence to factual accuracy) and utility (satisfying human needs and instructions) are both fundamental aspects of Large Language Models, yet these goals often conflict (e.g., sell a car with known flaws), which makes it challenging to achieve both in real-world deployments. We propose AI-LieDar, a framework to study how LLM-based agents navigate these scenarios in an multi-turn interactive setting. We design a set of real-world scenarios where language agents are instructed to achieve goals that are in conflict with being truthful during a multi-turn conversation with simulated human agents. To evaluate the truthfulness at large scale, we develop a truthfulness detector inspired by psychological literature to assess the agents' responses. Our experiment demonstrates that all models are truthful less than 50% of the time, though truthfulness and goal achievement (utility) rates vary across models. We further test the steerability of LLMs towards truthfulness, finding that models can be directed to be truthful or deceptive, and even truth-steered models still lie. These findings reveal the complex nature of truthfulness in LLMs and underscore the importance of further research to ensure the safe and reliable deployment of LLMs and LLM-based agents.