To avoid server side postbacks, use jquery to get the current dropdown's selected item, and based on that, use ajax to bind the second dropdown.
As this dropdown will be within a grid and the id generated dynamically, we need to use ClientID to get the referred dropdown.
<templatecolumn>
<itemtemplate>
<asp:dropdown id="ddl_main" runat="server" ...="" onchange="javascript:ddl_MainUpdated('#' + '<%ddl_main.ClientID%>', '#' + '<%ddl_child.ClientID%>' );" xmlns:asp="#unknown" />
<asp:dropdown id="ddl_child" runat="server" xmlns:asp="#unknown" />
</itemtemplate>
</templatecolumn>
javascript
function ddl_MainUpdated(mainDdlId, childDdlId) {
var selectedItem = $(mainDdlId + ' option:selected').text();
var listOfDependentItem = AjaxCall(selectedItem)
listOfDependentItem.each( function (index) { childDdlId.append( $(this).value ) } );</this>
Please note that this is just an illustration of how code would work.