Apparently, having tried it, that is not enough. You need to set minHeight / width, prefHeight / width and maxHeight / width to the same values.
As PrefHeight and Width are already set this works for me:
Public Sub SetLblFixedSize(Lbl As Label)
Dim MaxHeight As Double = Lbl.PrefHeight
Dim MaxWidth As Double = Lbl.PrefWidth
Lbl.as(JavaObject).RunMethod("setMaxHeight",Array(MaxHeight))
Lbl.as(JavaObject).RunMethod("setMaxWidth",Array(MaxWidth))
Lbl.as(JavaObject).RunMethod("setMinHeight",Array(MaxHeight))
Lbl.as(JavaObject).RunMethod("setMinWidth",Array(MaxWidth))
End Sub
Usage