In-context learning (ICL) capabilities are becoming increasingly appealing for building general intelligence due to their sample efficiency and independence from artificial optimization skills. To enhance generalization, biological neural systems primarily inherit learning capabilities and subsequently refine their memory, acquiring diverse skills and knowledge through extensive lifelong experiences. This process gives rise to the concept of general-purpose in-context learning (GPICL). Compared to standard ICL, GPICL addresses a broader range of tasks, extends learning horizons, and starts at a lower zero-shot baseline. We introduce two lightweight but insightful benchmarks specifically crafted to train and evaluate GPICL functionalities. Each benchmark includes a vast number of tasks characterized by significant task variance and minimal transferable knowledge among tasks, facilitating lifelong in-context learning through continuous generation and interaction. These features pose significant challenges for models that rely on context or interactions to improve their proficiency, including language models, decision models, and world models. Our experiments reveal that parameter scale alone may not be crucial for ICL or GPICL, suggesting alternative approaches such as increasing the scale of contexts and memory states.