We present results from the KMOS LENsing Survey (KLENS), which is exploiting gravitational lensing to study the kinematics of 24 star-forming galaxies at 1.4<z<3.5 with a median mass of log(M*/M_{sun}_)=9.6 and a median star formation rate (SFR) of 7.5M_{sun}/yr. We find that 25% of these low mass/low SFR galaxies are rotation-dominated, while the majority of our sample shows no velocity gradient. When combining our data with other surveys, we find that the fraction of rotation-dominated galaxies increases with the stellar mass, and decreases for galaxies with a positive offset from the main sequence (higher specific star formation rate). We also investigate the evolution of the intrinsic velocity dispersion, sigma_0_, as a function of the redshift, z, and stellar mass, M*, assuming galaxies in quasi-equilibrium (Toomre Q parameter equal to 1). From the z-sigma_0_ relation, we find that the redshift evolution of the velocity dispersion is mostly expected for massive galaxies (log(M*/M_{sun}_)>10). We derive a M*-sigma_0_ relation, using the Tully-Fisher relation, which highlights that a different evolution of the velocity dispersion is expected depending on the stellar mass, with lower velocity dispersions for lower masses, and an increase for higher masses, stronger at higher redshift. The observed velocity dispersions from this work and from comparison samples spanning 0<z<3.5 appear to follow this relation, except at higher redshift (z>2), where we observe higher velocity dispersions for low masses (log(M*/M_{sun}_)~9.6) and lower velocity dispersions for high masses (log(M*/M_{sun}_)~10.9) than expected. This discrepancy could, for instance, suggest that galaxies at high redshift do not satisfy the stability criterion, or that the adopted parametrization of the specific star formation rate and molecular properties fail at high redshift.