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Metal-based additive manufacturing techniques offer the ability to produce complex, near net shape parts that would be impossible or prohibitively expensive to manufacture via traditional casting and machining methods. Low density lattice structures for lightweight construction are one such example. However, there currently are no well-developed guidelines for designing and reliably manufacturing these structures. Literature on the topic is fragmented and usually only covers a limited aspect of the complex relations between process parameters, microstructure, lattice geometry and mechanical properties. This work covers the edge case of small diameter struts manufactured from AlSi10Mg via Laser Powder Bed Fusion (L-PBF) using the single contour exposure strategy, which is necessary to ensure sufficient geometric accuracy. Various cubic strut-based lattice geometries are manufactured using four laser parameter combinations corresponding to different area energy densities and beam offsets. The influence of process parameters and heat treatment on the microstructure and mechanical properties is investigated. Results show that the microstructure of filigree lattice struts can be tailored by the selection of process parameters, resulting in either uniform or core–shell structures depending on the laser power, while the macroscopic mechanical properties are mainly determined by the lattice geometry and relative density.