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.