If the penitent deliberately fails to confess a mortal sin, making the confession invalid, but confesses other mortal sins at the same time, will they the next time they go to confession need to confess the mortal sins they confessed last time as well the sin they failed to confess.
If a penitent deliberately fails to confess a mortal sin, as you say, the confession is invalid. That means that no sin was absolved, so, yes, the person will need to confess the fact that they withheld a mortal sin, all the mortal sins that they confessed during that invalid confession, and any other mortal sin that they may have committed since then.
They should not just confess all the mortal sins (those confessed and the one not confessed at the last confession), but also the one committed by withholding a mortal sin - stating “my last confession was a bad confession”, or something similar.
deliberately withholding a mortal sin makes the entire confession invalid, so the penitent would have to confess all mortal sins committed since the last valid confession. let us hope this hypothetical person does this without delay