If the strike is said to end at 7:11, would it actually end? It seems like this sort of thing would go on.
Tricky. If LH has rebooked your grandfather, then they have every intention of operating that flight. Chances are they have discussed this with the Union and there is a good chance the flight will go.
However this hard to predict with certainty. The aftermath of a strike is always a mess with 1000s of delayed/rebooked/displaced passengers and crews & equipment often being in the wrong place. It's very possible that the situation in FRA will be fairly chaotic at this time, so it depends a bit on how comfortable your grandfather would be in dealing with this.
Typically LH is pretty good with helping and assisting passengers who need help, but, again, after a strike there may be a lot more cases then they can handle.
but Lufthansa keeps wanting me to fly in Germany.
It should be very easy to route him through Austria or Switzerland (all part of the LH group) unless they are striking as well. Sometimes it helps if you find the right routing yourself and ask the agent on the phone to book it that way. Some agents are astonishingly bad at using their own systems and common sense.
Not sure if it makes to keep the current rebooking or keep trying to find another flight.
There is certainly no harm in trying and see if you can find something. Since LH has moved your schedule significantly you should be able to cancel for a full cash refund . If you can find something better at a somewhat affordable rate, then go for it.