By strongly hybridizing a high-finesse re-entrant cavity with an archetypal Ising magnet, LiHoF4, we perform microwave spectroscopic measurements on the electro-nuclear spin excitation spectra of the latter at dilution temperatures and high magnetic fields. We derive an explicit microscopic expression of the direct experimental observation by combining linear response theory [1] and the input-output formalism [2], without resorting to semi-classical approximations. With further help from mean field calculations of the eigen-states of LiHoF4, both with and without the random phase approximations, we obtain quantitative agreement between theoretical and experimental results across a wide range of parameter space. While the results provide strong support for existing hypotheses [3, 4] about the critical behavior of LiHoF4, they also reveal further mysteries regarding such a system that was previously considered well understood.