For some crystalline materials, a regime can be found where continuous ductile cutting is feasible. Using precision diamond turning, such materials can be cut into complex optical components with high surface quality and form accuracy. In this work we use diamond-turning to machine a monolithic, square-shaped, doubly-resonant LiNbO3 cavity with two flat and two convex facets. When additional mild polishing is implemented, the Q-factor of the resonator is found to be limited only by the material absorption loss. We show how our monolithic square resonator may be operated as an optical parametric oscillator that is evanescently coupled to free-space beams via birefringent prisms. The prism arrangement allows for independent and large tuning of the fundamental and second harmonic coupling rates. We measure 2.6 ± 0.5 dB of vacuum squeezing at 1064 nm using our system. Potential improvements to obtain higher degrees of squeezing are discussed.