Is this a well-studied problem? Problem: Optimally unlagging multiple time-series Is the problem of optimally lagging/unlagging multiple time-series with integer lags to maximize a sum of pairs of cross correlations or coherence an already well-studied problem? If so, references? Is it referred to with different names? 
Being able to define a notion of optimality seems important to me. Wouldn't one want to consider the cross power spectral densities and individual power spectral densities etc, in addition to maximizing weighted sums of pairs of correlations, where the weights are decided by the spectral densities? What would be a good approach to solve this problem of unlagging?
 A: Yes. Dynamic time warping (DTW) is often employed for that end. Basically, it's many variants try to minimize the 'distance' between timeseries (univariate or otherwise) shifting their indexes, but keeping their order.
A: More information is required to answer your question more specifically but essentially it appears you are attempting to model any kind of temporal dependence. In theory, multivariate SARIMA(p, d, q) × (P, D, Q) models will allow you to do this in a flexible matter. In a nutshell, you will choose values p, d, q, P, D, and Q, such that the residuals of your model show white noise behavior. Differencing is used to determine d, D while the rest of p, q, P, Q are chosen through autocorrelation and partial autocorrelation plots, and some model selection criteria such as AIC. SARIMA models do not always work best and you should assess the performance with simpler models, including naive models. Nonparametric models are also possible but model selection is different.
Good books on the subject matter are available.
