LH flight to Rome from LHR? Must be a code share unless you have another connection in Germany. I'd check as neither BA or Alitalia (the only airlines that fly LHR to Rome) are members of the same alliance as Air Canada. In fact I'd check that your onward flight is from LHR and doesn't involve a transfer to Gatwick.
But assuming that everything is OK then your luggage should be checked through all the way from US to Italy and so you can stay airside all the way to Rome EVEN if you don't get all your onward boarding cards.