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