As patron says, you can only use the RTW ticket on scheduled Star Alliance flights. Trying to take a flight on Condor on one of these tickets won't work, just as trying to take a flight on Tango wouldn't work, even though it is owned by Air Canada. Condor flights only appear in the Star timetable because members of the Lufthansa frequent flyer programme can earn and redeem miles on these flights (they should really be deleted!).

There is no way I can see you making it to BGI on a Star RTW ticket. You could fly to somewhere else in the Caribbean on UA, AC or MX, but even that would cause a problem if you're starting the ticket in North America (under the rules (see Patron's post above) you can't return to the continent you start from until you are finishing the flight).