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We investigate the magnetic phase diagram of 1T-vanadium dichalcogenide monolayers in Janus configuration (VSeTe, VSSe, and VSTe) from first principles. The magnetic exchange, magnetocrystalline anisotropy and Dzyaloshinskii-Moriya interaction (DMI) are computed using density functional theory calculations, while the temperature- and field-dependent magnetic phase diagram is simulated using large-scale atomistic spin modeling in the presence of thermal fluctuations. The boundaries between magnetic ordered phases and paramagnetic phases are determined by cross-analyzing the average topological charge with the magnetic susceptibility and its derivatives. We find that in such Janus monolayers, DMI is large enough to stabilize non-trivial chiral textures. In VSeTe monolayer, an asymmetrical bimeron lattice state is stabilized for in-plane field configuration whereas skyrmion lattice is formed for out-of-plane field configuration. In VSSe monolayer, a skyrmion lattice is stabilized for out-of-plane field configuration. This study demonstrates that non-centrosymmetric van der Waals magnetic monolayers can support topological textures close to room temperature.