I will assume that you are asking about getting into LSE, rather than through the program, given the wording for your post. A strong class rank will definitely help you, but the second most important factor will not be the GRE but the letters of recommendation. Of course generally speaking, great grades will imply strong letters, especially if you took challenging coursework. Explain to your professors why you want to do this program and have them comment on your suitability. Finally, the statement of purpose has barely any importance for a degree of this type. Just make sure it doesn't hurt you.