The benefits of not eating lamb and beef extend beyond the reduction in greenhouse gases to preserving the environment.
According to the Rainforest Partnership https://rainforestpartnership.org/the-beef-industry-and-deforestation/ the production of beef is without question the biggest cause of deforestation in the Amazon. With millions of acres of land devoted to the cultivation of soya beans for animal feed as well as the animal pastures created by clearing the forest, Brazil has become the biggest exporter of beef in the world.
Hence cutting down your consumption of hamburgers can help save the rain forests.
As to sheep, according to George Monbiot
Sheep have reduced most of our uplands to bowling greens with contours. Only the merest remnants of life persist. Spend two hours sitting in a bushy suburban garden and you are likely to see more birds and of a greater range of species than in walking five miles across almost any part of the British uplands. The land has been sheepwrecked.
By cutting back on your lamb kebabs you can contribute to the spread of biodiversity and the return of the natural world