Abstract: We have characterized a detector equipped with an undoped LaCl3 truncated cone crystal with dimensions of 22.5 mm in the largest diameter, 16 mm in the smallest diameter, and 16 mm in height, coupled to a fast Photonis XP2020/URQ photomultiplier tube (PMT). Its time response at 511 keV (Na-22) and Co-60 photon energies has been measured against a reference detector using a fast digitizer module by digital signal processing methods based on a genetic algorithm. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine-tuning of the digital parameters of the time pickup algorithm. The de-convoluted full width at half maximum (FWHM) time resolution is found to be 250 +/- 10 ps at Co-60 energies, and 444 +/- 8 ps using positron annihilation gamma-rays from 22Na, providing good prospects for the use of the crystal in applications requiring a fast time response.