I have a question for the case of E_{t-1} when the other equations are based on time t information.
For example, to estimate a LucasFuerst LP model,
one needs to include the optimality condition based at the time t-1 information as follows,

if the equation is conditional to the information in t-1, it must be setting one of the variables before knowing the innovations of period t. This variable should belong to period t-1, because, in Dynare, the variables are tagged with the period in which they are decided upon. In summary, after this change, at least one of the variables should be in t-1

Once, this is done, you can just shift forward in time the equation: (add one period to each variable). It is then conditional to the information in period t and you can write it as usual in Dynare