Additive manufacturing is especially suitable for complex-shaped 3D parts with integrated and optimized functionality realized by filigree geometries. Such designs benefit from low safety factors in mechanical layout. This demands ductile materials that reduce stress peaks by predictable plastic deformation instead of failure. Al–Cu wrought alloys are established materials meeting this requirement. Additionally, they provide high specific strengths. As the designation “Wrought Alloys” implies, they are intended for manufacturing by hot or cold working. When cast or welded, they are prone to solidification cracks. Al–Si fillers can alleviate this, but impair ductility. Being closely related to welding, Laser Beam Melting in Powder Bed (LBM) of Al–Cu wrought alloys like EN AW-2219 can be considered challenging. In LBM of aluminium alloys, only easily-weldable Al–Si casting alloys have succeeded commercially today. This article discusses the influences of boundary conditions during LBM of EN AW-2219 on sample porosity and tensile test results, supported by metallographic microsections and fractography. Load direction was varied relative to LBM build-up direction. T6 heat treatment was applied to half of the samples. Pronounced anisotropy was observed. Remarkably, elongation at break of T6 specimens loaded along the build-up direction exceeded the values from literature for conventionally manufactured EN AW-2219 by a factor of two.