To sync an LFO to the onset of a note, drive it with a phasor~ object. Send a phase value of "0" into the right inlet of phasor~ when the note starts, as seen in this example.
The MSP phasor~ object is frequently used as a low-frequency control signal for audio. Because it is often used to control other signals over a specific period of time, phasor~ can use tempo-relative timing, too. The frequency (rate) of a phasor~ is normally specified in Hertz, but you can alternatively give phasor~ a time interval, using tempo-relative time units, and it will use the inverse of that to determine its frequency.
If you want to change the coefficients of biquad~ in real time while a sound is playing, it's usually better to use MSP signals rather than individual Max messages, to avoid causing clicks. In that case, you should replace filtergraph~ with filtercoeff~ and send the frequency, gain, and Q parameters into filtercoeff~ as smooth signals (as shown in the left portion of the example).