Is lying about having a serious illness to conceal the reason for divorce and protect the children's reputation a sin that necessitates punishment or expiation?

You have done well in concealing your wife's sin. Lying is permissible to protect someone's property from an oppressor, and denying a sin is allowed to conceal one's own transgressions or those of others, as long as the person is not openly defiant. However, using dissimulation (Tawriya) is preferable. We advise you to reconcile with your wife if she has repented, for the sake of raising your children and concealing her past, as repentance erases what came before it.