Just applying to one school can be tough. LBS is a bit of a stretch for you, as they are gonna have a huge pool of people with similar background to choose from. But your experience and numbers are in place. so what you have to do is WOW them with your passion and make a really really really convincing argument for your absolute and total dedication to Social Venture Funds.
As for the international thing, yes LBS does look for it. How do you counter it? You don;t. You show as much as possible whatever you have (i.e. working in other languages, taking business trips, working with people from other countries, etc.)
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