Lightweight structures are susceptible to vibration due to their reduced mass. However, conventionally used techniques to avoid high vibration amplitudes (such as increasing the mass and/or applying damping mechanisms) are contradictory to the original goal of designing a lightweight structure. An increase of eigenfrequencies above external, exciting frequencies helps to prevent resonance phenomena. Here, we use a combined design and optimisation method to generate irregular lattice structures to investigate their potential of reaching much higher eigenfrequencies than those of regular structures, while retaining low weight and high stiffness. We generate parametric constructions of lattice structures with different degrees of structural irregularities, including regular lattices with constant and functionally graded strut cross-sections, and irregular lattices. Evolutionary strategic optimisation is used to maximise the first eigenfrequency. Geometric restrictions associated with selective laser melting are considered, and three optimised lattice structures are manufactured in selective laser melting using aluminium (AlSi10Mg). Their eigenfrequencies are measured in vibration experiments with a shaking table. Our approach allows the efficient generation of more than 500 lattice structures. The results show that by using irregular lattice structures, the first eigenfrequency is increased by 58% compared to a regular lattice structure of the same mass. The numerically obtained eigenfrequencies coincided well with the experimental results. It is argued that the implementation of higher degrees of structural irregularities allows the development of solutions with even higher first eigenfrequencies. In conclusion, we show that irregular lattice structures have a high potential to manipulate the eigenfrequencies of lightweight structures.