The physical properties of LuAsO4, such as structural, electronic, linear optical, dynamic, and thermodynamic properties, have been studied under pressure using the density functional theory within the local density approximation. The calculations of electronic band structure of the crystal show that it is an insulator with an indirect band gap value of 4.1977 eV at zero pressure and that the value of band gap increase by increasing pressure. The linear optical properties of the crystal, dependent on the frequency of incoming light, have been calculated. The components of dielectric tensor, static dielectric constant, and refractive index have been calculated under pressure while some optical constants such as energy loss function, extinction coefficient, absorption coefficient, reflectivity, effective dielectric constant, and effective number of valence electrons have been calculated at zero pressure. Moreover, the phonon dispersion, some thermodynamic potentials such as free energy, internal energy, and some thermodynamic properties such as entropy and heat capacity have been calculated under pressure.