Multivariate - Time series data pattern changes
One starting approach is doing the cross-correlation as you've said. The correlation will fail to capture the time shifted behavior. But you should calculate it for every pair of Milk/Drug you have.

The ccf() function in R does it for you.

If you're not successful i suggest you to take a look at the multiple time-series plotted side by side (like here) and check if really there exists this time-shifted pattern in your customer behavior.