Lattice structures can present advantageous mechanical properties while remaining remarkably lightweight. Precise lattice design can however be tricky to set up on arbitrary domain with classical 3D modeling methods as it involves very fine oriented details. Interestingly, natural porous structures can present such lattice-like design which motivates the seek for bio-inspired approaches. In this paper we present a novel method to grow lattice-like structures within an arbitrary shape and aligned along an oriented field using adapted Reaction/Diffusion systems. While not directly computed from a global optimization process our structures still demonstrate remarkable structural properties for which we provide examples with numerical validation.