In the context of developing new rotorcraft dedicated to Advanced Air Mobility, the use of non-conventional propulsive systems such as coaxial counter-rotating rotors, equipped or not with a shroud, is often addressed. The present numerical study falls into this framework. We actually propose to analyse the noise generated by such configuration in stationary conditions with a direct noise simulation realized thanks to a lattice Boltzmann Method. In a first step, the predictions are validated by comparisons with measurements realized in an anechoic chamber for the unshrouded case. A good agreement is observed on both tonal and broadband components of the noise radiated by the propulsive system. Then, the effects of using a shroud around the rotors are investigated numerically. It appears that the use of the shroud significantly increases the relative importance of the broadband noise because of interactions between turbulent wakes with the rear propeller and the duct surface. One can consequently conclude that employing a shroud is not necessarily a good option and this architectural choice must be made carefully. Finally, the impact of the rotor-rotor distance is analysed in both cases with and without shroud. As expected, increasing the distance allows reducing the noise levels but this effect seems to be limited to the tonal noise with almost no impact on the broadband component. Those observations are still valid when the duct is used, but placing the front rotor closer to the shroud inlet makes the shrouded configuration even louder. In a near future, this study will be completed by a complementary test campaign that will allow more validations of the present simulations and confirm or not the resulting conclusions.