Is it necessary to place the lids of the elution tube and column into the slots of the rotor adapter during processing on the QIAcube Connect?

Yes, this is absolutely necessary. If the lids are not securely fixed in the rotor adaptor slots during processing on the QIAcube Connect, they will detach from the elution tubes and columns during centrifugation, and will collect at the bottom of the centrifuge chamber.