The Italian strategy is simply to try to prevent running out of ICU beds or at least minimize the number of people that can't get IC in the short-term due to the current uncontrolled spread.

As far as I can tell, what to do long-term is still up to debate, and continuing the lockdown only for higher-risk/older people is certainly an option.

Note however that jumping straight to such a differentiated lockdown seems much less likely to work, because behavior changes are easier in a total lockdown with full media and discourse focusing on it, as well as much easier enforcement since you don't have to distinguish the high-risk people.