We present theoretical results for the expected fraction of Lyman Break Galaxies (LBGs) to be detected as strong Lyman alpha emitters (LAEs) in the redshift range 5 < z < 7. We base our analysis on the 2-billion particle SPH simulation MareNostrum High-z Universe. We approximate galaxies as static dusty slabs with an additional clumpy dust distribution affecting stellar populations younger than 25 Myr. The model for the Lyman alpha escape fraction is based on the results of our Monte-Carlo radiative transfer code (CLARA) for a slab configuration. We also fix the transmission of Lyman alpha photons through the intergalactic medium to a constant value of 50% at all redshifts. From the results of this model we calculate xLya, the fraction of Lyman Break Galaxies with Lyman alpha equivalent width (EW) larger than 50 Angstrom. We find a remarkable agreement with observational data at 4.5 < z < 6. For bright (-22 < MUV < -20.5) and faint (-20.5 < MUV < -18.5) galaxies our model predicts xLya = 0.02 \pm 0.01 and xLya = 0.47 \pm 0.01 while observers report xLya = 0.08 \pm 0.02 and xLya = 0.47 \pm 0.16, respectively. Additional evolution of the extinction model at redshift z \sim 7, that decreases the intensity of transmitted Lyman alpha radiation by a factor of f_T = 0.4 as to match the LAE luminosity function at z \sim 6.5, naturally provides a good match for the recently reported xLya fractions at z > 6.3. Exploring different toy models for the Lyman alpha escape fraction, we show that a decreasing Lyman alpha escape fraction with increasing UV galaxy luminosity is a key element in our model to explain the of larger xLya fractions for fainter LBGs.