CX can tag your luggage to LHR at HKG if you show them your BA ticket. They may be able to issue boarding passes for BA, but probably not. Presumably BA FRA-LHR is a separate ticket. If you miss the BA flight, for whatever reason, it is your problem and how BA treats you depends on what fare you paid. Worst case you have to buy a new ticket (at full fare); BA is somewhat prone to do this on restricted fares. By buying a separate ticket you are absorbing the risk of being late for the flight. FRA is a huge airport and I think CX and BA are at opposite ends (so it takes about 20 minutes just to transit the airport, never mind any processing time). This year winds have been high, making westbound flights an hour late (and eastbound an hour early). Your chances of making the connection at 1.5 hours is about 10% in my opinion (and I often book such tight connections), and I would book a later flight.