system.nav.openWindowInstance returns a reference to the newly opened window, use that reference instead of calling system.gui.getWindow, like such:
targetWindow = system.nav.openWindowInstance("Popup windows/Loft/DrumInspectionScreen")
Additionally, don't write to and then read from the same tag in the same script. Use variables to store temporary data, that's what they do. The assignment to drumno.selectedIndex can be simplified to drumno.selectedIndex = value - 1, and the call to system.tag.readBlocking can be removed.
Overall your code can be simplified to the following (with more descriptive names for the variables):
def onDoubleClick(self, rowIndex, colIndex, value, event):
if rowIndex == -1:
return
tableData = self.data
firstColValue = tableData.getValueAt(rowIndex, 0)
system.tag.writeAsync(["[client]ScadaNavigation/DrumSelectLime"], [firstColValue])
newPopup = system.nav.openWindowInstance("Popup windows/Loft/DrumInspectionScreen")
drumNoComponent = newPopup.getComponentForPath("Root Container.lbo_Drums")
drumNoComponent.selectedIndex = firstColValue - 1
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EDIT: Added cleaned code, corrected selectedIndex assignment example