I'm not so sure that they won't cancel the rest of your booking. I once missed a flight as part of a LONE4 due to a misunderstanding following a change of date (the QF agent I spoke to booked me on the wrong date).

The flight missed was an AA service from ELP to ORD and I then had further flights to BOS//DCA-MIA-NAS-LHR-MXP, all on AA except for the last two segments on BA.

AA canceled my ORD-BOS & DCA-MIA flights following the missed segment. The BA segments were untouched, though, as was the MIA-NAS on AEagle.

I tried to find out what actually happened but with no success... Nevertheless AA rebooked me on the next available services at no extra charge (with an additional change in YYZ on the ORD-BOS run)