I am not nearly as familiar with Lyrica (pregablin) as I am with Neurontin (gabapentin), but they are similar drugs, with pregablin carrying a greater potency and a somewhat different range of effects. There is quite a body of information on the use of gabapenin to control benzo withdrawal symptoms on the web in general, but not vice versa. I myself have been on numerous frustrated searches.
In my experience, benzos do help immensely with gabapentin WD and most likely that of pregablin. I once woke up in the back of an ambulance after a grand mal seizure when I discontinued clonazolam and gabapentin simultaneously. I was in the hospital left with the restlessness and intense vertigo characteristic of gabapentin WD. I recieved some powder etizolam in the mail that day and upon returning home, moving ever so slowly so that the room wouldn't flip upside down, I managed to dose approximately 3-5 mg (accounting for the previously abused clonazolam's cross-tolerance). The dizziness and other WD symptoms resolved quite quickly and I was able to fall asleep.
This anecdote should provide some assurance that benzos can circumvent a variety of gaba-related withdrawals, but it is worth noting that many will make claims to the contrary, as gabapentin WD specifically involves some unique and stubborn symptoms. Outside of my personal experience, I have read/heard that pregablin WD is much worse. Also, from what I understand, 1200-2000 mg of Lyrica is a very high dose.