The lamb represents passive, uncomplaining submission even in suffering, of following without reservation. Isaiah 53:7 says of Christ, "He was oppressed and He was afflicted, yet He opened not His mouth; He was led as a lamb to the slaughter, and as a sheep before its shearers is silent, so He opened not his mouth."
Jeremiah makes a similar statement about an episode in his life: "But I was like a docile lamb brought to the slaughter; and I did not know that they had devised schemes against me, saying, 'Let us destroy the tree with its fruit, and let us cut him off from the land of the living, that his name may be remembered no more'" (Jeremiah 11:19). This does not mean he did nothing but that he was innocent of being the cause of the persecution inflicted upon him and that he accepted it without griping about his lot as God's servant.
In Romans 8:36, this symbolism is directly applied to us, "For [God's] sake we are killed all day long; we are accounted as sheep for the slaughter." God expects us to follow the example of our Leader and others who have gone before us. Having this submissive attitude is not for destruction—even though on the surface it may seem that way—but following is necessary for preparation. Hebrews 5:7-10 reminds us that Christ also had to submit to be prepared for His responsibilities as our High Priest. We must consider following uncomplainingly as a necessary part of being a whole burnt offering. It is "not my will, but Yours be done" in practical application.