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Laser powder bed fusion enables the fabrication of complex components such as thin-walled cellular structures including lattice or honeycomb structures. Numerous manufacturing parameters are involved in the resulting properties of the fabricated component and a material and machine-dependent process window development is necessary to determine a suitable process map. For cellular structures the thickness, which correlates with the process parameters, directly influences the mechanical properties of the component. Thus, dimensionless scaling laws describing the correlation between strut thickness, process parameters, and material properties enable predictive lattice structure design for laser powder bed fusion. This contribution develops material independent dimensionless allometric scaling laws for both single track and contour exposure to enable process-driven design of lattice structures in laser powder bed fusion. The theory derived with dimensional analysis is validated for the powder alloys stainless steel alloy 1.4404, nickel alloy 2.4856, aluminum alloy AlSi10Mg and Scalmalloy AlMgSc. The results can be used for the process-driven design of lattice structures and dense material obtaining high precision in the micrometer range or economic production with high melt pool widths.