Compatibility summary
You will need a travel adapter in Luxembourg; plug types used there differ from Singapore.
Plug comparison
Singapore plug types: G
Luxembourg plug types: C F
There is no common plug type between Singapore (G) and Luxembourg (C F). You need a travel adapter.
Voltage comparison
Singapore: 230V, 50Hz
Luxembourg: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.