We present a study of the solvation of lanthanoid(III) ions in liquid dimethylsulfoxide (DMSO) using molecular dynamics simulations employing a newly developed polarizable force field. The van der Waals (vdW) parameters were obtained for La$^{3+}$ and Lu$^{3+}$ (the first and the last in the lanthanoids(III) series) using ab initio data. The parameters of the other ions can be extrapolated based on physical considerations without additional (and costly) quantum chemistry calculations. This extrapolation procedure has been successfully applied to Gd$^{3+}$. The outcomes of our simulations turn out to be in agreement with both the experimental data available in the literature and the ab initio results. A small adjustment of the vdW parameters further increases the agreement with experiments and has allowed us to provide structures, geometrical parameters and coordination numbers. For heavy lanthanoids (Gd and Lu) we obtain clearly an 8-fold coordination, with a distorted square anti prism (SAP) geometry in agreement with EXAFS and XANES experiments; for the La$^{3+}$ ion, our force field predicts a mixed situations with both the 8-fold SAP and 9-fold geometry where the SAP structure is capped by a ninth molecule added over one face.