We present the first Lyman Alpha Emitter (LAE) study that combines: (i) cosmological SPH simulations run using GADGET-2, (ii) radiative transfer simulations (CRASH), and (iii) a previously developed LAE model. This complete LAE model accounts for the intrinsic LAE Lyman Alpha/continuum luminosity, dust enrichment and Lyman Alpha transmission through the intergalactic medium (IGM), to quantify the effects of reionization, dust and velocity fields on the Lyman Alpha and UV Luminosity Functions (LF). We find that a model neglecting dust sorely fails to reproduce either the slope or the magnitude of the observed Lyman Alpha and UV LFs. Clumped dust is required to simultaneously fit the observed UV and Lyman Alpha LFs, such that the intrinsic Lyman Alpha-to-continuum luminosity is enhanced by a factor f_alpha/f_c ~ 1.5 (3.7) excluding (including) peculiar velocities. The higher value including velocity fields arises since LAEs reside in large potential wells and inflows decrease their Lyman Alpha transmission. For the first time, a degeneracy is found between the the ionization state of the IGM and the clumping of dust inside high-redshift galaxies. The Lyman Alpha LF at z ~ 5.7 can be well reproduced (to within a 5 sigma error) by a wide range of IGM average neutral hydrogen fraction, 3.4/10^3 to 0.16, provided that the increase in the Lyman Alpha transmission through a more ionized IGM is compensated by a decrease in the Lyman Alpha escape fraction from the galaxy due to dust absorption. The physical properties of LAEs are presented, along with a discussion of the assumptions adopted.