According to Oatmeal - Free VSTi Synth - Togeo Studios
in the "MIDI Control" or "Main Screen" pictures, the LFO shows a mode called "Global-Free". "Free" in this case means "free-running" - e.g. it keeps on doing its thing regardless of what note you play.
The alternative would most likely be called "key trigger" or "gate" - this means it restarts its cycle every time you press a key. If you can change this option (and there's no reason to present it if free running was the only option), try doing so. If you're using the default skin all it may be labeled in a slightly different way.
It also shows a very small black circular button below the "RATE UNIT" in that same screenshot with the text "Quantize". My (hopefully) educated guess is that this changes the LFO timing from milliseconds to notes - and then you should be able to select quarter notes, 8ths, 16ths, whatever you want.
Oatmeal doesn't have a great user interface - well, definitely not with the default skin. Consider KVR: Synth1 by Ichiro Toda - Details
as well - better labels on the buttons, bigger knobs.