Check out general rules https://www.lufthansa.com/us/en/extended-rebooking-options
For new bookings, it says
For flights booked on or after August 25, all fares of the Lufthansa
Group airlines worldwide can be rebooked free of charge (except for
travel originating in Japan). This is part of your fare conditions,
which you can view at any time. The departure and destination airports
can also be changed.* If the rebooked fare is more expensive due to a
change of route or a necessary change of travel or booking class, an
additional charge may be necessary.
The key sentence here is
This is part of your fare conditions, which you can view at any time.
That means when you book the flight there will be a lot of fare conditions, rules, and fine print that you will need to agree to. This rules will spell out the details: how often you can rebook, to what degree you can change destinations, what happens for over/underpayments, departure and return time windows, etc. This may vary by ticket to ticket, so you may have to do some "almost" bookings and check the rules carefully when they are displayed.
Typically you can change the travel date until before the original departure date to any legal return date that's available at the time of rebooking. At this point the price for the new itinerary is calculated the same way as if you would buy the new ticket from scratch. Then they calcualted the difference between the new fare and the original one. If the new ticket is cheaper, you may get the difference back, keep it for future travel or the airline will just pocket it. Again, that depends on the fare rules for your specific ticket. However, in most cases the new ticket is more expensive and you have to pay the difference out of pocket.
There is no price protection whatsover, the new ticket can (and often will) be substantially more expensive than your original one. It's also quite possible that the price difference may be more expensive than just booking a full new ticket with another carrier.
If I were you, I'd wait until the November return date becomes available and then shop around for the best options for the entire trip.