Tangent flows at singularities for locally almost calibrated solutions to Lagrangian mean curvature flow in C^2 are modelled on unions of static planes, and all singularities are of Type II. To understand the finer singularity structure at such singularities it is thus necessary to understand all possible limit flows. As an essential step in this direction we show that any ancient solution with a blow-down a union of two static multiplicity one planes, meeting along a line has to be a translator. Together with previous work together with Lambert and Lotay this gives a full picture of all ancient solutions with entropy less than three. This is joint work with J. Lotay and G. Szekelyhidi.