Under standard conditions, the transfer time is already plenty. Under current conditions, it should be even more than enough.
All Star Alliance flights (that includes all Lufthansa flights; excluding flights to Israel) arrive and depart from terminal 2. In essence, terminal 2 is a long building with a passport checking area in the middle. A satellite ...
LH uses a terminal in Munich that has been built to their specification to make such short transfers possible. 1h 10min is actually rather generous even, as the minimum for Munich is 30 minutes.
So yes, you will be fine. And in the unlikely event that your inbound is delayed LH will put you on the next available flight.