By Anna Yukhananov WASHINGTON (Reuters) - As French Finance Minister in 2010, Christine Lagarde opposed the involvement of the International Monetary Fund in Greece. Now as the country stands on the edge of defaulting on a 1.6 billion euro (£1.14 billion) payment to the Fund, Lagarde's tenure at the head of the IMF since 2011 will be shaped by Greece, which holds a referendum on Sunday that could pave the way to its exit from the euro. It ended up endorsing austerity measures proposed by the European Commission and European Central Bank, its partners in the troika of Greece's lenders, instead of leading talks as it had done with other countries such as Russia and in the Asian financial crisis.