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We report on the spatial response characterization of large LaCl$_{3}$(Ce) monolithic crystals optically coupled to 8$\times$8 pixel silicon photomultiplier (SiPM) sensors. A systematic study has been carried out for 511 keV $\gamma$-rays using three different crystal thicknesses of 10 mm, 20 mm and 30 mm, all of them with planar geometry and a base size of 50$\times$50 mm$^2$. In this work we investigate and compare two different approaches for the determination of the main $\gamma$-ray hit location. On one hand, methods based on the fit of an analytical model for the scintillation light distribution provide the best results in terms of linearity and field of view, with spatial resolutions close to $\sim$1 mm FWHM. On the other hand, position reconstruction techniques based on neural networks provide similar linearity and field-of-view, becoming the attainable spatial resolution $\sim$3 mm FWHM. For the third space coordinate $z$ or depth-of-interaction we have implemented an inverse linear calibration approach based on the cross-section of the measured scintillation-light distribution at a certain height. The detectors characterized in this work are intended for the development of so-called Total Energy Detectors with Compton imaging capability (i-TED), aimed at enhanced sensitivity and selectivity measurements of neutron capture cross sections via the time-of-flight (TOF) technique., Comment: Accepted Manuscript Elsevier / CC-BY-NC-ND