I assume that each respondent only selects one department. (because you say "dropdown question")
Here you can have two questions, the dropdown and the matrix in one group.
In the matrix you can display the employees by subquestion relevance.
and after selecting a department:
If you want to select multiple departments, use a multiple question and create the matrices for each department.
With question relevance display the matrices of the selected departments.
BTW: Which version of LS do you use?
Joffm