If it's long haul and you're well dressed you will stick out like a sore thumb
As Zed3 mentions, it was once the case that there was a fairly strict dress code for ID pax, especially in Business or First. It was easy to pick out who were the ID pax and who were the fare paying pax! I know that in latter years things were relaxed up to a point and I believe jeans are accepted as long as they are not scruffy or ripped etc. I think that jacket and tie is no longer a requirement but t-shirts are not accepted. I'm no longer acquainted with LH dress code. Why not contact their staff travel office and ask them.