Hey there,
You seem to have a pretty good profile, here are some things that work out for you:
Academics ,UG rank and GMAT look great. .CFA works as a good differentiator.
Work experience is pretty interesting as well. Having an international exposure and an analytical background will definitely add value to your profile, if you are showcase these experiences properly through your application.
Having said that, most of the applicants who apply to schools like LSE and MIT do have a stellar profile, so in a lot of ways, even with a good profile you may be starting at level ground.
Your essays will play a key role in differentiating you from the rest of the applicants, so make sure that you are spending enough time on them ( Usually 12-15 days).
With a strong application, I would say that LSE is possible. Secondly, you have mentioned just LSE and MIT as your target schools. It is always a better strategy target at least 4-6 schools categorized into dream, competitive and safe as per your profile.
In case you need some in-depth insights about different aspects of your profile that will help you in doing this, you can check out this profile evaluation tool:
https://mim-essay.com/profile-evaluation?gcf