Here we introduce a compact holographic microscope embedded onboard a Lab-on-a-Chip (LoC) platform. A wavefront division interferometer is realized by writing a polymer grating onto the channel to extract a reference wave from the object wave impinging the LoC. A portion of the beam reaches the samples flowing along the channel path, carrying their information content to the recording device, while one of the diffraction orders from the grating acts as an off-axis reference wave. Polymeric micro-lenses are delivered forward the chip by Pyro-ElectroHydroDynamic (Pyro-EHD) inkjet printing techniques. Thus, all the required optical components are embedded onboard a pocket device, and fast, non-iterative, reconstruction algorithms can be used. We use our device in combination with a novel high-throughput technique, named Space-Time Digital Holography (STDH). STDH exploits the samples motion inside microfluidic channels to obtain a synthetic hologram, mapped in a hybrid space-time domain, and with intrinsic useful features. Indeed, a single Linear Sensor Array (LSA) is sufficient to build up a synthetic representation of the entire experiment (i.e. the STDH) with unlimited Field of View (FoV) along the scanning direction, independently from the magnification factor. The throughput of the imaging system is dramatically increased as STDH provides unlimited FoV, refocusable imaging of samples inside the liquid volume with no need for hologram stitching. To test our embedded STDH microscopy module, we counted, imaged and tracked in 3D with high-throughput red blood cells moving inside the channel volume under non ideal flow conditions.