Yes, he lies.
All day, everyday.
Both to protect his secret identity, and his considerably less powerful loved ones from the potentially severe reprisals of his enemies.
FFS, see what happened when Luthor figures out Clark's secret in DAWN OF JUSTICE: both Lois and Martha were immediately kidnapped.
People always yap about "Truth, Justice, and the American Way", and they always hound the American Way part as problematic when really it's the truth that Supes does not stand for in its purest form.
But there's never been any doubt about the justice part.