While I can sympathize with his plight, why didn't he get at least one extra set of clothes immediately? If he needed the correct upgraded attire for business right away, well, that's the cost of business. It's unrealistic to expect that the luggage, once "lost" would catch up in time.

As for "compensation", this is one that is pretty well laid out in the contract of carriage, and it's not all that much. What may be interesting is whether or not this falls under the US or EU rules since the outbound was on BA, but the ticket was US. I leave that to someone more experienced.