Experimental assessment of the strain tensor within a microstructure is challenging, especially for small mechanical deformations acting over submicron length scales. In this work, we fully characterize the spatial strain distribution within a suspended micro-disk laser made of Ge1-xSnx alloy, with fine resolution< 200 nm. We employ Scanning X-ray Diffraction Microscopy, a model-free method based on synchrotron radiation, to directly obtain maps of all components of lattice strain and rotation, including the shear strains, finding them on a magnitude~ 10-3. We correlate these small elastic deformations to structural defects and the relaxation of the three-dimensional microstructure, demonstrating the potential of an advanced X-ray microscopy technique for microelectronics.