By Conor Humphries and Marc Jones DUBLIN/FRANKFURT (Reuters) - The European Central Bank increased its funding lifeline to Greece's banks again on Tuesday, sources with direct knowledge of the decision said, allowing the country's banks to stay open as Athens inches towards a deal with creditors. It raises the amount of Emergency Liquidity Assistance (ELA) to around 89 billion euros ($100 billion), a growing liability that is worrying many around the euro zone.