We investigated magnetic vortices in two stoichiometric LiFeAs samples by means of scanning tunneling microscopy and spectroscopy. The vortices were revealed by measuring the local electronic density of states at zero bias conductance of samples in magnetic fields between 0.5 and 12 T. From single vortex spectroscopy we extract the Ginzburg-Landau coherence length of both samples as 4.4±0.5 nm and 4.1±0.5 nm, in accordance with previous findings. However, in contrast to previous reports, our study reveals that the reported hexagonal-to-squarelike vortex lattice transition is absent up to 12 T both in field-cooling and zero-field-cooling processes. Remarkably, a highly ordered zero-field-cooled hexagonal vortex lattice is observed up to 8 T. We argue that several factors are likely to determine the structure of the vortex lattice in LiFeAs such as (i) details of the cooling procedure, (ii) sample stoichiometry that alters the formation of nematic fluctuations, (iii) details of the order parameter, and (iv) magnetoelastic coupling.