I don't think that's right. There is a basic theorem in (untyped) lambda calculus that says that if a term has a normal form, then any evaluation strategy, including strict and non-strict, will reduce that term to that normal form. Since non-strict evaluation can "skip" arguments that may have no normal form, there are expressions in non-strict languages that terminate while their strict counterparts don't. The opposite scenario does not exist: if a term has to be evaluated, it has to be done in both the strict and non-strict versions. (And in simply typed lambda calculus, all reduction sequences terminate.)

For (actual) programming languages without mutation and with more than just lambdas and application for control flow, it is right:

    f x y = y
    f (raise Done) Ω

Under lazy application semantics this program will never terminate. Under eager application semantics it will.