"(being analog in nature) still suffers the "unnoticeable" lag"

Not really... Remember that digital circuitry also doesn't switch from 0 to 1 or 1 to 0 in zero time! It is physically impossible to do that. It is why your PC goes hot. Time is required to change from high to low and vice versa, no matter if the circuit generating the transition is analog or digital in nature. Even a pushbutton does not go from open to closed with a sharp edge of absolutely 0 seconds. The time required is not called "lag" but RISETIME.

From personal experience: I have built many circuits where an opamp comparator (remember to provide some positive feedback in order to get a hysteresis, or else you are in danger of noise causing a burst of pulses on the output!!!!!) directly drove an input pin, and I have never had problems with it.