This paper focuses on the evaluation of a microchannel-plate photomultiplier tube (MCP-PMT) as a candidate detector, suitable for positron lifetime studies. Several properties of MCP-PMTs, such as their fast time response, compact size, low susceptibility to magnetic fields, relatively high gain and the low power consumption make them attractive for positron lifetime spectroscopy. The preliminary tests were performed with a 85001-501 Burle PlanaconTM photomultiplier tube assembly. Initial measurements were conducted with a pulsed Picosecond Injection Laser (PiLas) system. The engineering sample of the 85001 exhibits a transit-time-spread (TTS) of 110 ps (FWHM). Further timing experiments showing the suitability of the device as Cherenkov detector are presented. For the first time, a conventional positron lifetime spectrum of a Cz-Si probe measured with a spectrometer, where an MCP-PMT detector is included, has been demonstrated.