Most prior motion prediction endeavors in autonomous driving have inadequately encoded future scenarios, leading to predictions that may fail to accurately capture the diverse movements of agents (e.g., vehicles or pedestrians). To address this, we propose FutureNet, which explicitly integrates initially predicted trajectories into the future scenario and further encodes these future contexts to enhance subsequent forecasting. Additionally, most previous motion forecasting works have focused on predicting independent futures for each agent. However, safe and smooth autonomous driving requires accurately predicting the diverse future behaviors of numerous surrounding agents jointly in complex dynamic environments. Given that all agents occupy certain potential travel spaces and possess lane driving priority, we propose Lane Occupancy Field (LOF), a new representation with lane semantics for motion forecasting in autonomous driving. LOF can simultaneously capture the joint probability distribution of all road participants' future spatial-temporal positions. Due to the high compatibility between lane occupancy field prediction and trajectory prediction, we propose a novel network with future context encoding for the joint prediction of these two tasks. Our approach ranks 1st on two large-scale motion forecasting benchmarks: Argoverse 1 and Argoverse 2.