Van der Waals stacking has provided unprecedented flexibility in shaping many-body interactions by controlling electronic quantum confinement and orbital overlap. Theory has predicted that also electron-phonon coupling critically influences the quantum ground state of low-dimensional systems. Here we introduce proximity-controlled strong-coupling between Coulomb correlations and lattice dynamics in neighbouring van der Waals materials, creating new electrically neutral hybrid eigenmodes. Specifically, we explore how the internal orbital 1s-2p transition of Coulomb-bound electron-hole pairs in monolayer tungsten diselenide resonantly hybridizes with lattice vibrations of a polar capping layer of gypsum, giving rise to exciton-phonon mixed eigenmodes, called excitonic Lyman polarons. Tuning orbital exciton resonances across the vibrational resonances, we observe distinct anticrossing and polarons with adjustable exciton and phonon compositions. Such proximity-induced hybridization can be further controlled by quantum designing the spatial wavefunction overlap of excitons and phonons, providing a promising new strategy to engineer novel ground states of two-dimensional systems. Here, the authors demonstrate proximity-controlled strong-coupling between Coulomb correlations and lattice dynamics in neighbouring van der Waals materials (WSe2 and a gypsum layer), creating electrically neutral hybrid exciton-phonon eigenmodes called excitonic Lyman polarons.