The Talbot interferometer using white synchrotron radiation has already been demonstrated for high-speed X-ray phase imaging and tomography as well as four-dimensional phase tomography for an observation of a dynamic specimen. In those previous experiments, the grating lines were oriented horizontally because the synchrotron radiation source size is large in the horizontal direction, and only the vertical spatial coherence satisfies the requirement for the operation of the Talbot interferometer given its distance from the source. For non-rigid samples, the horizontal axis of rotation causes unwanted motion of the sample due to gravity which results to artifact in the tomography reconstruction. For fluid samples, a vertical rotation axis is certainly necessary. While it is possible to orient the sample rotation axis perpendicular to the grating lines of the Talbot interferometer, solving the definite integral of the differential phase images to obtain the phase shift for x-ray phase tomography proves to be cumbersome when the sample extends outside the image and there is no null region for which the integration constant is known. In this work we aimed at increasing the spatial coherence of the x-rays along the horizontal so that the grating lines and the sample rotation axis could be oriented vertically. A Talbot-Lau interferometer was constructed by adding an absorption grating which acted as vertical line sources of horizontally spatially coherent white synchrotron radiation to the Talbot interferometer. An average of 20% moiré fringe visibility was obtained. The set-up was demonstrated for highspeed phase tomography of a polymer sample.