The menisci sit on the top of the tibia. The lateral (outer) meniscus is more 'O-shaped' than the medial meniscus, which is more 'C-shaped'. It is also more mobile and has an intimate relationship to the tendon of the popliteus muscle.
Important anatomical differences
The lateral meniscus and popliteus tendon form part of the 'posterolateral corner', where injuries may be a challenge to the surgeon because of the complexity in this region. The lateral meniscus differs considerably from the medial meniscus. It is O-shaped, rather than C-shaped, and is much more mobile than the medial meniscus and there is much less attachement around the outer rim to the capsular walls. In addition, the tendon of the popliteus muscle passes between the outer rim at the back of the meniscus and the capsule.
Cysts of the lateral meniscus. Crowell MS, Westrick RB and Fogarty BT. Int J Sports Phys Ther. 2013 Jun; 8(3): 340–348.
Associated tears of the lateral meniscus in anterior cruciate ligament injuries: risk factors for different tear patterns. Feucht MJ, Bigdon S, Bode G, Salzmann GM, Dovi-Akue D, Südkamp NP, and Niemeyer P. J Orthop Surg Res. 2015; 10: 34.