We study young star-forming clumps on physical scales of 10 - 500 pc in the Lyman-Alpha Reference Sample ( LARS ) , a collection of low-redshift ( z = 0.03 - 0.2 ) UV-selected star-forming galaxies . In each of the 14 galaxies of the sample , we detect clumps for which we derive sizes and magnitudes in 5 UV -optical filters . The final sample includes \sim 1400 clumps , of which \sim 600 have magnitude uncertainties below 0.3 in all filters . The UV luminosity function for the total sample of clumps is described by a power-law with slope \alpha = -2.03 ^ { +0.11 } _ { -0.13 } . Clumps in the LARS galaxies have on average \Sigma _ { SFR } values higher than what observed in HII regions of local galaxies and comparable to typical SFR densities of clumps in z = 1 - 3 galaxies . We derive the clumpiness as the relative contribution from clumps to the UV emission of each galaxy , and study it as a function of galactic-scale properties , i.e . \Sigma _ { SFR } and the ratio between rotational and dispersion velocities of the gas ( v _ { s } / \sigma _ { 0 } ) . We find that in galaxies with higher \Sigma _ { SFR } or lower v _ { s } / \sigma _ { 0 } , clumps dominate the UV emission of their host systems . All LARS galaxies with Ly \alpha escape fractions larger than 10 \% have more than 50 \% of the UV luminosity from clumps . We tested the robustness of these results against the effect of different physical resolutions . At low resolution , the measured clumpiness appears more elevated than if we could resolve clumps down to single clusters . This effect is small in the redshift range covered by LARS , thus our results are not driven by the physical resolution .