Rapid mass assembly, likely from mergers or smooth accretion, has been predicted to play a vital role in star formation in high-redshift Lyα emitters. Here, we predict the major merger, minor merger and smooth accreting Lyα emitter fraction from z ≈ 3 to 7 using a large dark matter simulation and a simple physical model that is successful in reproducing many observations over this large redshift range. The central tenet of this model, different from many of the earlier models, is that the star formation in Lyα emitters is proportional to the mass accretion rate rather than the total halo mass. We find that at z ≈ 3 nearly 35 per cent of the Lyα emitters accrete their mass through major (3:1) mergers, and this fraction increases to about 50 per cent at z ≈ 7. This implies that the star formation in a large fraction of high-redshift Lyα emitters is driven by mergers. Comparing our predictions with observations, we find that the model-predicted fractions are relatively larger. While there is discrepancy between the model predictions and observed merger fractions, some of this difference (˜15 per cent) can be attributed to the mass-ratio used to define a merger in the simulation. We predict that future, deeper observations which use a 3:1 definition of major mergers will find ≥30 per cent major merger fraction of Lyα emitters at redshifts ≥3.