We report on the direct generation of optical vortex lattice (OVL) modes from a diode-pumped Pr3+:LiYF4 (Pr:YLF) laser achieved by employing off-axis (transverse) and defocused (longitudinal) pumping geometries in the laser medium. OVL modes with more than 40 phase singularities are generated. The experimentally observed OVL modes are well supported by a theoretical analysis based on the superposition of Hermite-Gaussian modes. We also discuss the intracavity frequency doubling of the OVL modes. The proposed OVL mode laser system can be applied to fundamental optical science and advanced material engineering.