Two points:
1. You probably already know this, but your LFO must be clock synched to an EVEN MULTIPLE DIVISION of the clock to have the same phase when the beat comes around again - 1/4, 1/8, 1/16, that sort of thing. Triplets or dotted or swung divisions won't (necessarily, depends on your bar length) come back around evenly. That's just how math works, of course. If you want a slower or faster LFO than that, well, mathematically it won't line up with the beat the same way.
2. Your sequencer should probably always transmit clock - if the sequencer stops clock and then resumes play off-beat (e.g. asynchronously) with the clock phase of where it was last stopped (compared to if the clock kept running, that is) then the LFO which free-syncs in the meantime (or, I think on some DSI models, I don't have a Pro 2 to be certain, stops entirely if it's synced, which would put the phase wherever it was last when it stopped) then the *frequency* will match the beat but the *phase* won't, and you get another version of the same problem you're discussing.
There is not to my knowledge a way to reset the LFO phase *only on START/PLAY* unless as @quatschmacher said, you also send the nrpn to do so at the same time. The Deluge can't do this, so you're stuck with either note sync or nothing since the Deluge isn't actually a particularly fluent sequencer (I have one, I know this to be very true) but rather a groovebox with some half-baked sequencing features thrown in for fun.