Charge density wave (CDW) states in solids bear an intimate connection to underlying fermiology. Modification of the latter by a suitable perturbation provides an attractive handle to unearth novel CDW states. Here, we combine extensive magnetotransport experiments and first-principles electronic structure calculations on a non-magnetic tritelluride LaTe$_{3}$ single crystal to uncover phenomena rare in CDW systems: $(i)$ hump-like feature in the temperature dependence of resistivity at low temperature under application of magnetic field, which moves to higher temperature with increasing field strength, $(ii)$ highly anisotropic large transverse magnetoresistance (MR) upon rotation of magnetic field about current parallel to crystallographic c-axis, (iii) anomalously large positive MR with spike-like peaks at characteristic angles when the angle between current and field is varied in the bc-plane, (iv) extreme sensitivity of the angular variation of MR on field and temperature. Moreover, our Hall measurement reveals remarkably high carrier mobility $sim$ 33000 cm$^{2}$/Vs, which is comparable to that observed in some topological semimetals. These novel observations find a comprehensive explication in our density functional theory (DFT) and dynamical mean field theory (DMFT) calculations that capture field-induced electronic structure modification in LaTe$_{3}$. The band structure theory together with transport calculations suggest the possibility of a second field-induced CDW transition from the field-reconstructed Fermi surface, which qualitatively explains the hump in temperature dependence of resistivity at low temperature. Thus, our study exposes the novel manifestations of the interplay between CDW order and field-induced electronic structure modifications in LaTe$_{3}$, and establishes a new route to tune CDW states by perturbations like magnetic field.
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