If you study the references you'll find the locking range is defined as the range where the oscillator will frequency lock onto an incoming signal, and this is defined as:
delta F = +-[Fo/(2Q)](Ii/Ib),
where Fo is the free running oscillator frequency, Q is the oscillator loaded Q, Ii is the injected signal current and Ib is the oscillator bias current.
This delta frequency range is where the phase between the injected signal Ii and oscillator signal is between +-90 degrees. The oscillator can hold lock slightly beyond delta F and this is shown with the Phase peaks above and below +-90 degrees.
In the plot shown below you can see where the DSO has some trouble and the amplitude and phase are jittering around the lock range edges. The markers indicate the ~ +-90 phase and show a delta frequency of 2.56KHz which agrees with the 2*(1.347KHz) = 2.69KHz predicted from the notes.
This measurement is particularly difficult for the DSO to perform since the oscillator signal is large and near the Input Signal frequency, so the DSO must dig out the reference signal, and frankly we're surprised this DSO can perform this measurement, and speaks highly of the Frequency Selective Sampling Technique utilized. Honestly, we did not expect these results!!
Anyway, this is an involved subject as you can tell, Razavi does a nice job and recommended as a reference.
Best,