Spectral hp/element methods have gained recent prominence in simulating high Reynolds (Re) number incompressible flows around complex, 3D industrial geometries. Efficient preconditioning techniques are needed to alleviate the computational cost of the iterative solution of these methods, facilitating their adoption in industrial applications. This work presents a high-performance, scalable preconditioning technique, called the Lower-order refined (LOR) preconditioner, for the Poisson problem. This preconditioner addresses the decoupled pressure equation system in the incompressible Navier-Stokes equations solver within the open-source spectral/hp element method framework Nektar++. LOR preconditioner, also known as the SEMFEM preconditioner, uses a spectrally equivalent lower-order (p=1) discretisation to precondition the high-order problem. This preconditioner utilizes lower-order operator sparsity for cheaper operator evaluations and a constant memory requirement per degree of freedom. It shows minimal sensitivity to high aspect-ratio elements, making it suitable for complex geometries. The LOR preconditioner exhibits a bounded iterative condition number with increasing problem size for rectangular and hexahedral elements. This work addresses the previous gaps in the literature, as the LOR preconditioner is demonstrated for spectral/hp elements in Nektar++, using a modal expansion basis for triangle elements in 2D and prismatic and tetrahedron elements in 3D - in addition to quadrilaterals in 2D and hexahedrons in 3D. The conditioning properties of these element types are evaluated for different LOR mesh point distribution approaches using suitable test cases of increasing complexity relevant in the context of race-car aerodynamics. Finally, the performance of the LOR preconditioner is analysed in practice by solving a Poisson problem for the said test cases.