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Understanding the escape of Lyman continuum (LyC) and Lyman alpha (Lya) photons from molecular clouds is one of the keys to constraining the reionization history of the Universe and the evolution of galaxies at high redshift. Using a set of radiation-hydrodynamic simulations with adaptive mesh refinement, we investigate how photons propagate and escape from turbulent clouds with different masses, star formation efficiencies (SFEs), and metallicities, as well as with different models of stellar spectra and supernova feedback. We find that the escape fractions in both LyC and Lya are generally increasing with time if the cloud is efficiently dispersed by radiation and supernova feedback. When the total SFE is low (1% of the cloud mass), 0.1-5% of LyC photons leave the metal-poor cloud, whereas the fractions increase to 20-70% in clouds with a 10% SFE. LyC photons escape more efficiently if gas metallicity is lower, if the upper mass limit in the stellar initial mass function is higher, if binary interactions are allowed in the evolution of stars, or if additional strong radiation pressure, such as Lya pressure, is present. As a result, the number of escaping LyC photons can easily vary by a factor of $\sim4$ on cloud scales. The escape fractions of Lya photons are systemically higher (60-80%) than those of LyC photons despite large optical depths at line centre ($\tau_0\sim10^6-10^9$). Scattering of Lya photons is already significant on cloud scales, leading to double-peaked profiles with peak separations of $v_{\rm sep}\sim400\,{\rm km\,s^{-1}}$ during the initial stage of the cloud evolution, while it becomes narrower than $v_{\rm sep} \le 150 \, {\rm km\,s^{-1}}$ in the LyC bright phase. Comparisons with observations of low-redshift galaxies suggest that Lya photons require further interactions with neutral hydrogen to reproduce their velocity offset for a given LyC escape fraction.