<p>Wait, I think I’m misunderstanding your question. So basically, is it possible for you to not leave, stay in their program, and continue studying, but at the same time apply to Duke? If so, obviously, I think that would be the best option. </p>
<p>While you’re writing the application though, I think it’s pretty apparent that you should focus on Duke, and how badly you wanted to attend, and the heartbreaking news that you were waitlisted, and then rejected, etc. and how you’ve changed/grown a lot since that time. Basically, forget about LSE while you’re doing the application, and talk about Duke (but don’t lie). Also, make sure you’re thorough in your application, because people will pay attention to those small details. </p>
<p>Then, once you’ve gotten the acceptance, at that point you can start to decide which school you really want to attend, because you’ll have a clearer vision with the acceptance “green light”. LSE is also a very prestigious school. Dont’ know if this helps at all, but good luck!</p>