The properties of a 50 mm x 50 mm x 30 mm monolithic LaBr3:Ce scintillator crystal coupled to a position-sensitive multi-anode photomultiplier (PMT, Hamamatsu H9500),representing the absorbing detector of a Compton camera under study for online ion (proton) beam range verification in hadron therapy, was evaluated in combination with either absorptive or reflective crystal surface coating. This study covered an assessment of the energy and position-dependent energy resolution, exhibiting a factor of 2.5-3.5 improvement for the reflectively wrapped crystal at 662 keV. The spatial dependency was investigated using a collimated Cs-137 source, showing a steep degradation of the energy resolution at the edges and corners of the absorptively wrapped crystal. Furthermore, the time resolution was determined to be 273 ps (FWHM) and 536 ps (FWHM) with reflective and absorptive coating, respectively, using a Co-60 source. In contrast, the light spread function (LSF) of the light amplitude distribution on the PMT segments improved for the absorptively wrapped detector. Both wrapping modalities showed almost no differences in the energy-dependent photopeak detection efficiency.