Analysis of repeated measures when fixed effect changes within-subjects?

I'm helping a colleague with a repeated-measures analysis in which each
subject's fixed effect changes over the course of data collection.  He's
measuring a continuous, positive response variable (`Response`) in
agricultural plots (`ID`) (which themselves are grouped within `Blocks`) as
a function of `Crop` type.  The response variable is measured 4 times over
the course of the season.  The analysis would normally look something like
this:

    modelout <- lmer(Response ~ Crop + (Month|ID) + (1|Block) ,
                     data=cropdata, family=gamma(link="inverse"))

However, just to make things complicated, the first measurement is done
prior to planting, so it's influenced by the *previous year's* crop type.
That is, for plot A1, Month 1's `Crop` is Wheat, but Month 2-4's `Crop`
types are Barley.  Is there any way to analyze this in a single model?