I bought the ticket several months ago. What you contracted for was your transportation from origin airport to destination airport on a given day. That contract still stands, check the T&Cs. Perhaps 5 minutes earlier than you had expected, Lufthansa will get you to where you plan to go - or make alternative arrangements or provide compensation, in just the same way for a 45 minute connection that goes sour as they would have for a 50 minute connection that went sour.
You may think the risk of missing your connection has changed significantly but clearly Lufthansa consider there to be enough time. Bear in mind it takes time to fill an aircraft with passengers. If a planeload delay turning up at the gate until the time schedule for take off, the flight will be delayed. Hence gates 'closing' before ETD. But the people who 'close' gates are able, if they see fit, to hold open or re-open for connecting passengers. Once missed connections are the airlines responsibility you may be amazed at how little time is necessary to make a connection. First of all you will have about an additional 20 minutes (the time required to load every other passenger but you) between the rule that applies in general and what is likely to apply to a connecting passenger. Then you may have a few more minutes between when the aircraft should have been fully loaded, before the doors are sealed. Then there is also the possibility of delaying take off (though this is not likely unless there are several other passengers in a similar situation to you).
If your first flight is delayed for example, and depending to some extent on where you are going, there is even the possibility of a Lufthansa representative waiting for you on arrival in Frankfurt and shepherding you through in very much less time than you might expect. They may drive you to the control points and have you jump queues.
can I get 100% reimbursement of my non-reimbursable ticket?
No. "I have changed my mind" is not enough for that.
Do I have a right to request that?
Of course, but you would probably be wasting your time. It is just possible that Lufthansa has realised, since you booked, that your flight out of FRA risks being overbooked, say, hence would welcome your rescheduling but the chances of such are not good. In all probability it would make little difference to them which flight out you choose, but rebooking you would cost them more than they would be inclined to suffer.
can I ask to modify the dates for free?
Again, you can ask but it is likely to make no difference. They are not obliged to accommodate a change, are not inclined to waste their money and would not want to set a precedent for others.
Lufthansa's Terms & Conditions - General Conditions of Carriage (Passenger and Baggage) (yours may differ) include within 9.1:
If, after you purchase your Ticket, we make a significant change to the scheduled flight time, which is not acceptable to you, you will be entitled to a refund in accordance with Article 10.2.
For reasons as outlined above, you will not be able to establish that 5 minutes is significant.
A chart might summarise much of the detail above:
It is optimistic to assess driving (maybe in an electric cart) as half the time of walking but there is also less chance of wasting time finding the right route and, in some airports, the possibility of taking a route not generally available to the public. A long time ago I went from an enquiry desk to aircraft via a walk through the building interstices and a car ride across the tarmac, bypassing control points (CPs). No check in, no Passport Control and no Security (and not even a ticket).