Depending upon the local jurisprudence of course, Triumph lingerie cannot prevent you from using Triumph-America.com . In Canada there was a court case where Mattel sued a restaurant called Barbie's for trade mark infringement. The courts ruled that since Mattel's business was toys and not restaurants there would be no confusion between the brands. There was also a more well known court case where Apple, a music production company owned by the Beatles tried to sue Apple (Mac) unsuccessfully again do to the fact that their businesses were different.
You would of course have to stop using the web address if Triumph Motorcycles told you to.