Photonic integrated circuits provide a scalable platform for photonics-based quantum technologies. However, integrating quantum emitters and electro-optic cavities within this platform remains an open challenge proving to be a major hurdle from implementing key functionalities for quantum photonics, such as single photon sources and nonlinearities. Here, we address this shortcoming with the hybrid integration of InAs/InP quantum dot emitters on foundry silicon photonics and the implementation of photonic crystal cavities in thin-film lithium niobate. Co-integrated on-chip electronics allow us to tune the emission properties of the quantum dots while enabling GHz-rate coherent modulation over photons trapped in the cavities, thus providing a new level of programmability over interactions between optical fields and atom-like systems in integrated circuits. Our results open the door to a new generation of quantum information processors that can be manufactured in leading semiconductor foundries.