Fast cross correlation with limited range
If the limited range is significantly more than log(N) shorter than the total signal of length N, then ordinary cross correlation over that limited range may be faster than FFT-based fast correlation.  You could just iterate away from the estimated/predicted lag until you find you have gone past a correlation peak (by a sufficient amount to account for expected noise).  But if you go more than log(N)/2 points away from your initial estimate, then perhaps switch back to fast convolution cross correlation.