You will have to go through passport control as you are exiting the Schengen zone. This in and of itself can easily soak up the 1:40 that you have available to you.
Not to mention the time it takes to cover the distance from gates A -> Terminal Lobby -> Passport Control -> C -> Gate 15
Now the good news is that everyone at the airport will know which flights are departing and you will most likely be put on a priority queue if there is a long line at immigration (this is really, your only real cause of concern).
Your luggage will be transferred automatically, as you are on one ticket.
Personally, 1:40 is a bit tight for my liking - but as the airline has booked you the itinerary, it is their responsibility to make sure you reach your destination.
Lets assume the worse case scenario that your flight is delayed in-bound, and there is a long queue at immigration, and by the time you clear all that and find your way to the gate, the flight has departed.
Before any of that happens though:
You'll notice people running around yelling the flight number and destination of your flight.
You'll see someone that is minding the queue at immigration, and they will be calling for people with flights close to departure.
Your name may be called as well.
Once the flight has departed:
a. Lufthansa will arrange to put you on the next available flight.
b. Depending on how long the delay is to your next flight; you may be provided compensation.
So, the worse that will happen is that you will be bumped to a later flight along with some compensation.