The recent discovery of extreme magnetoresistance in LaSb introduced lanthanum monopnictides as a new platform to study topological semimetals (TSMs). In this work we report the discovery of extreme magnetoresistance in LaBi, confirming lanthanum monopnictides as a promising family of TSMs. These binary compounds with the simple rock-salt structure are ideal model systems to search for the origin of extreme magnetoresistance. Through a comparative study of magnetotransport effects in LaBi and LaSb, we construct a triangular temperature-field phase diagram that illustrates how a magnetic field tunes the electronic behavior in these materials. We show that the triangular phase diagram can be generalized to other topological semimetals with different crystal structures and different chemical compositions. By comparing our experimental results to band structure calculations, we suggest that extreme magnetoresistance in LaBi and LaSb originates from a particular orbital texture on their qasi-2D Fermi surfaces. The orbital texture, driven by spin-orbit coupling, is likely to be a generic feature of various topological semimetals.