Thanks for the advice, however, this is what I found after excitedly opening up Live to test your suggestion:
While I can make the right-click menu appear for the sync'd LFO rate by right clicking the clock divider in the display section to the right of the LFO rate knob, adding this parameter to the automation list and changing the clock rate does not make the parameter appear in Live's automated parameter list. I can make the parameter appear in Live when it is not sync'd, so that fact coupled with Jorg's comment above that this technique is not possible still leads me to believe we are missing this feature.
Please let me know if you find otherwise!