No, but it can be retriggered by MIDI Note On messages or by divisions of a MIDI Clock signal.
The Voyager’s signal path is 100% analog, including its LFO and envelopes. Therefore, there is no way to make the LFO rate sync precisely to a digital signal. However, if the LFO sync knob is set to MIDI, the LFO will be retriggered at each MIDI clock division, in a manner similar to hard sync on the oscillators.
This can create some interesting effects, especially when the LFO rate is slower than the rate of the clock divisions, as it will not finish its complete cycle before restarting. In this case, the LFO acts more like a looping envelope whose shape can be adjusted by changing the rate. And you can change the number of clock divisions in EDIT mode.
A similar effect can be achieved each time a MIDI note is sent by setting the LFO sync knob to KB (Keyboard).