This is a version of the LFO MIDI Max 4 Live object included with Ableton Live 9, that allows you to automate the rate parameter when set to sync, as several users reported that it wasn’t possible to do this with the original version.
Download LFOMIDI-JG.amxd
For those who want to fix it themselves I have included a screenshot below showing the dial to be configured and the field that needs to be set to “automated and stored” in the object’s inspector: