Generally, an optical vortex lattice (OVL) is generated via the superposition of two specific vortex beams. Thus far, OVL has been successfully employed to trap atoms via the dark cores. The topological charge (TC) on each optical vortex (OV) in the lattice is only ±1. Consequently, the orbital angular momentum (OAM) on the lattice is ignored. To expand the potential applications, it is necessary to rediscover and exploit OAM. Here we propose a novel high-order OVL (HO-OVL) that combines the phase multiplication and the arbitrary mode-controllable techniques. TC on each OV in the lattice is up to 51, which generates sufficient OAM to manipulate microparticles. Thereafter, the entire lattice can be modulated to desirable arbitrary modes. Finally, yeast cells are trapped and rotated by the proposed HO-OVL. To the best of our knowledge, this is the first realization of the complex motion of microparticles via OVL. Thus, this work successfully exploits OAM on OVL, thereby revealing potential applications in particle manipulation and optical tweezers. © 2021 Liuhao Zhu et al., published by De Gruyter, Berlin/Boston 2021.