I switched to Levemir some two weeks ago because I used to wake up low with Lantus, and it also didn't cover 24 hours for me. It worked out for the past years but circumstances in my life have changed, so I thought it was time to consider a change in insulin, too.
I'm not sure, if my lows were due to "peaks", in fact I think it's rather Levemir that has peaks than Lantus. But maybe that goes for me but not for everyone, we're all different.
True is that it seems to take a while for Lantus to start.
I never had sudden drops in bs that were caused by Lantus - except for my morningly lows, but I have these with levemir, too, just not as severe as with Lantus which is a progress, I guess. Though, in my case it was most likely due to the fact that it didn't cover 24 hours and my body ran out of Lanus before I took the next dose.
In your case, I'd say it was the NoroRapid... it is also possible that your bs was on it's way down anyway and the Novorapid did what was left over to do.