LXeGRIT - Liquid Xenon Gamma-Ray Imaging Telescope - is the first prototype of a Compton telescope for MeV g-ray astrophysics based on a LXe time projection chamber. One of the most relevant figures of merit for a Compton telescope is the detection efficiency for g-rays, which depends on diverse contributions such as detector geometry and passive materials, trigger efficiency, dead time, etc. A detailed study of the efficiency of the LXeGRIT instrument, based both on laboratory measurements and Monte Carlo simulations, is presented in this paper.