TOKYO, June 2 : The U.S. dollar steadied on Tuesday as markets took a wait-and-see approach to Middle East peace talks, with Lebanon announcing a limited ceasefire between Hezbollah and Israel, although broader geopolitical uncertainties kept traders on edge.  Investors have treated any progress toward ending the Iran conflict with caution, given the fragility of a U.S.–Iran ceasefire struck in early April. The dollar index, which measures the currency against six peers, eased from earlier