© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. We present adaptive optics-assisted integral field spectroscopy around the Hα or Hβ lines of 12 gravitationally lensed galaxies obtained with VLT/SINFONI,Keck/OSIRIS and Gemini/NIFS. We combine these data with previous observations and investigate the dynamics and star formation properties of 17 lensed galaxies at 1 < z<4. Thanks to gravitational magnification of 1.4-90 times by foreground clusters, effective spatial resolutions of 40-700 pc are achieved. The magnification also allows us to probe lower star formation rates (SFRs) and stellar masses than unlensed samples; our target galaxies feature dust-corrected SFRs derived from Hα or Hβ emission of ~0.8-40M⊙ yr-1, and stellar masses M* ~ 4 × 108-6 × 1010 M⊙. All of the galaxies show velocity gradients, with 59 per cent consistent with being rotating discs and a likely merger fraction of 29 per cent, with the remaining 12 per cent classed as 'undetermined'. We extract 50 star-forming clumps with sizes in the range 60 pc-1 kpc from the Hα (or Hβ) maps, and find that their surface brightnesses, Σclump and their characteristic luminosities, L0, evolve to higher luminosities with redshift. We show that this evolution can be described by fragmentation on larger scales in gas-rich discs, and is likely to be driven by evolving gas fractions.