Recent advances in reinforcement learning (RL) have increased the promise of introducing cognitive assistance and automation to robot-assisted laparoscopic surgery (RALS). However, progress in algorithms and methods depends on the availability of standardized learning environments that represent skills relevant to RALS. We present LapGym, a framework for building RL environments for RALS that models the challenges posed by surgical tasks, and sofaenv, a diverse suite of 12 environments. Motivated by surgical training, these environments are organized into 4 tracks: Spatial Reasoning, Deformable Object Manipulation & Grasping, Dissection, and Thread Manipulation. Each environment is highly parametrizable for increasing difficulty, resulting in a high performance ceiling for new algorithms. We use Proximal Policy Optimization (PPO) to establish a baseline for model-free RL algorithms, investigating the effect of several environment parameters on task difficulty. Finally, we show that many environments and parameter configurations reflect well-known, open problems in RL research, allowing researchers to continue exploring these fundamental problems in a surgical context. We aim to provide a challenging, standard environment suite for further development of RL for RALS, ultimately helping to realize the full potential of cognitive surgical robotics. LapGym is publicly accessible through GitHub (https://github.com/ScheiklP/lap_gym).