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We compute string theoretic black hole solutions having Lifshitz asymptotics with a general dynamical exponent z > 1. We start by constructing solutions in a flux compactification of six dimensional supergravity, then uplift them to massive type IIA supergravity. Alongside the Lifshitz black holes we study the simpler anti-de Sitter solutions, of which there are a 1-parameter family in this supergravity, and compare and contrast their properties. The black holes are characterized by a two-form and scalar charge, and we numerically explore their configuration space and thermodynamical aspects. ; STFC/ST/J000426/1 ; theWolfson Foundation and Royal Society ; Perimeter Institute for Theoretical Physics ; DFG/GRK/1463 ; STFC/ST/H005498/1