They can.
Cap values and cap hits are two very different things. Dak's new deal could have him average $56 million annually. But the Cowboys can make $20 million or more of that a signing bonus, then spread the cap hit out from that across the length of the contract. Same for Lamb and Micah.
Kicking the can down the road does hurt sometimes- remember the Cowboys still had Tony Romo on the cap for three years after he retired. But with the cap also set to increase every season, this is very doable. Not easy, but certainly doable.