In the "really lean, really tasty" category here in the US, you might consider Buffalo. Also, the Broken Arrow Ranch website offers a number of options for game meat, such as venison and wild boar.
https://brokenarrowranch.com/?gad_source=1"This venison comes from truly wild and free-roaming South Texas Antelope, Axis Deer, and Fallow Deer. All animals are field harvested using a mobile processing unit. These species produce venison that is extremely lean and of the highest quality"