High-order Computational Fluid Dynamics (CFD) methods have the potential to deliver higher accuracy at lower computational cost than conventional second-order methods. In this work, we introduce Lethe, an object-oriented, open-source, high-order (space and time) CFD software which leverages the well-established deal.II library. Lethe solves incompressible flow problems on 2D and 3D unstructured quad and hex meshes and allows dynamic mesh adaptation. It is parallel and it is adapted to the solution of large problems (>108 degrees of freedom) on distributed computer architectures. We illustrate some of its fundamental capacities through two benchmarks: a manufactured solution and the DNS of Taylor–Green vortices at Re=1600.