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Low X-ray Luminosity Galaxy Clusters. III: Weak Lensing Mass Determination at 0.18 $<$ z $<$ 0.70

This is the third of a series of papers of low X-ray luminosity galaxy clusters. In this work we present the weak lensing analysis of eight clusters, based on observations obtained with the Gemini Multi-Object Spectrograph in the $g'$, $r'$ and $i'$ passbands. For this purpose, we have developed a pipeline for the lensing analysis of ground-based images and we have performed tests applied to simulated data. We have determined the masses of seven galaxy clusters, six of them measured for the first time. For the four clusters with availably spectroscopic data, we find a general agreement between the velocity dispersions obtained via weak lensing assuming a Singular Isothermal Sphere profile, and those obtained from the redshift distribution of member galaxies. The correlation between our weak lensing mass determinations and the X-ray luminosities are suitably fitted by other observations of the $M-L_{X}$ relation and models.