Convey time lag information to a linear regression model
Linear regressions have fixed number of variables. An alternative could be to run a separate regression for each item group, and add a different number of time lags for each. If you can't do that, I suggest you to find an optimal number of time lags to be chosen for this general model. You can take a look at ACF, and specifically PACF plots to understand how much memory (time dependency) your time series have.

In theory, adding a more time lags should't result in a problem: if the n-th time lag is not relevant to explain your y, then it's parameter will show no statistical significance.