I discovered a bug in the LFO component in Guitar Rig 7.0.2. Since the last GR software update was 2 years ago, I'm almost certainly wasting my breath, but hopefully this post might help someone else from pulling their hair out, if they encounter the same issue.
If you open the GR7 VST plugin (in your DAW, or Maschine), and set GR's internal metronome to "Sync: Extern", then it will sync perfectly (and correctly) with the host. It will not only match the tempo, but also the phase (or playback position). For example, restarting host playback from 00:00 will restart the metronome from beat 1. So far, so good.
Now load an LFO instance, with the default settings. You'll also need to assign the LFO to something (drag-and-drop the assignment icon onto a parameter on some other component), in order to see the LFO's output. In the LFO, turn on "Tempo Sync". Leave "Auto" and "S.C." off (those are for syncing the LFO to an audio signal). The LFO output should follow GR's metronome, but it doesn't. It will oscillate at the correct tempo, but will not match the phase of GR's metronome. For example, if you restart host playback from 00:00, the LFO will continue oscillating from wherever it happens to be at the time (instead of resetting to phase 0, as it should).
This is pretty disappointing, as it makes it impossible to reliably sync the LFO with your DAW (or even GR7's internal metronome). And of course it means that the "LFO Phase Offset" parameter is useless. The best workaround, I suppose, is to use your DAW's automation, instead of GR7's LFO component.
I've confirmed that this was working correctly (i.e. no bug) in Guitar Rig 5.2.2. I'm not sure about GR6.
I'll admit that this is a fairly esoteric bug, in software which is no longer being updated… but in my defence, this is a Native Instruments forum. :-)