Summary: How fast does the interaction take place? is it like carbamazepine, cranking up over a few weeks? or immediate? And what dose of divalproex is sufficient to begin the interaction?
Answer: immediate; at 250-500 mg in adults.
From this reference in 1992:
Inhibition of lamotrigine metabolism is already maximal at dosages of valproate around 500 mg day−1, and results in an approximate twofold increase in serum lamotrigine levels [38–40]. Because the risk of lamotrigine-induced skin rashes is dependent on the rate of rise of serum lamotrigine concentration, in patients comedicated with valproate lamotrigine should be initiated at reduced dosages (in adults, 25 mg on alternate days) and titrated more slowly to target dosages which are lower than those used in patients not taking valproate. Although there is no risk of rash when valproate is added on in a patient already stabilized on lamotrigine, neurotoxic effects may occur if the dosage of the latter is not reduced by about 50% as soon as the dosage of valproate reaches, in an adult, about 250–500 mg day−1.