The considerable thing to do is to ask your girlfriend. If she is embarrassed at all by your appearing without a tie while being surrounded by everybody else who wears one. If she dose not care, then you must not worry in the slightest. But if she were to be conscious of your standing out, then you should either suggest lunching elsewhere or dumping her for her shallowness.
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Circumnavigator, lawyer and columnist and the man who divides his time between Singapore, Hong Kong and China. I believes that etiquette transcends nationality and race. 
In this column I will offer stylish advice to everyday questions on etiquette at work and at home and anything else that may be bothering you.