A telescope works by converting photon directions into positions on the film (Parabolic reflector). In the opposite direction, a wide viewing angle display placed where the film goes will produce a parallel projection of the image as a beam, such that no matter where you stand looking into the beam, the image will appear in the same direction. This is the same as if the image were projected on a screen at infinity. Even clouds will look fine, because they are not really distinguishable from images infinity. The sun or moon will stay in the same direction, and the light it projects will all be parallel, making realistic shadows.
So all you need is a parabolic reflective ceiling, a suitably placed mirror (perhaps above a chandelier) reflecting into a sufficiently bright display (the display could go directly near the focus, but a secondary mirror would be easier to hide. A sufficiently large and bright LED screen might be practical today, but it would not be able to emulate the sun's intensity. Instead, we might use a separate high intensity light source such as a sulphur plasma light on an arm that tracks across the image.
(And parabolic arches are a great shape for ceilings because they ensure that there is no shear force inside the structure)