Over recent decades, electricity demand has experienced sustained growth through widespread electrification of transportation and the accelerated expansion of Artificial Intelligence (AI). Grids have managed the resulting surges by scaling generation capacity, incorporating additional resources such as solar and wind, and implementing demand-response mechanisms. Altogether, these policies influence a region's carbon intensity by affecting its energy mix. To mitigate the environmental impacts of consumption, carbon-aware optimizations often rely on long-horizon, high-accuracy forecasts of the grid's carbon intensity that typically use compute intensive models with extensive historical energy mix data. In addition to limiting scalability, accuracy improvements do not necessarily translate into proportional increases in savings. Highlighting the need for more efficient forecasting strategies, we argue that carbon forecasting solutions can achieve the majority of savings without requiring highly precise and complex predictions. Instead, it is the preservation of the ranking of forecasts relative to the ground-truth that drives realized savings. In this paper, we present LiteCast, a lightweight time series forecasting method capable of quickly modeling a region's energy mix to estimate its carbon intensity. LiteCast requires only a few days of historical energy and weather data, delivering fast forecasts that can quickly adapt to sudden changes in the electrical grid. Our evaluation in 50 worldwide regions under various real-world workloads shows that LiteCast outperforms state-of-the-art forecasters, delivering 20% higher savings with near-optimal performance, achieving 97% of the maximum attainable average savings, while remaining lightweight, efficient to run, and adaptive to new data.