No. If you no-show for a flight, the later flights are cancelled.
You need to consider why LAX-LHR-NCE rtn is cheaper than LAX-LHR return.
Some of it might be cheaper taxes in france for a deparature from NCE.
Another element might be a cheaper quoted fare to take people to NCE.
See if stop overs are permitted for a fee in the fare rules, then go:
LAX-LHR (multi day stop over) LHR-NCE (same day turn around or overnight) NCE-LHR-LAX.
While you could also consider:
LAX-LHR-NCE (same day turn around or overnight) NCE-LHR (Mult day Stop over) LAX.
- the taxes would be higher here.
Otherwise just see how much it would cost to nest NCE-LON-NCE inside your flight.