You want to use the Bamboo Cross List Web Part to aggregate and display different fields from all three lists in a single View.
Step 1:
Create a SharePoint custom List as your Project List, for example:

Step 2:
Create a Department List, for example:

Step 3:
Create a SharePoint Task List. Your Tasks List contains the lookup fields to the Project and Department lists that were created above:

Note that the lookup fields from the Task List can link to any field from the Project or Department List, for example:

Create items in your list. Your Task List should look similar to this:

Step 4:
Install the Bamboo Cross List Web Part according to instructions in the Application Notes. Once the Web Part is installed, select Modify Shared Web Part from the menu accessed at the upper right corner of the Web Part. This menu is only accessible by users with authority to modify the page.

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Select the Task list as your Parent list. Pick a View that contains the appropriate data that you want to use.
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Select the first lookup list "Project List" and an associated View (All Items in this example).
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Select the second lookup list, "Department List", and an associated View.
As you select the lookup list, you should see the list data displayed in the scroll list below:


Step 4:
Select the columns that you want to display in the combined Vew. Use the arrow keys and the Up and Down keys to align your information.

When you are done with the selection, press Apply and OK to close the Web Part's setting page.
Step 5:
The Bamboo Cross List Web Part displays the combined data from the three selected Lists in a single View. Note that you can click on any linked field, such as Title with link, to go directly to that particular List item.

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