LH/LX: ORD-DUB in F ~$4500, can involve extended stay in FRA/MUC
 

This fare has been available for a while, but I found that it's possible to arrange the flights to make a quick side trip to Dublin and return to Germany, if that is your primary destination for the majority of the trip. Requires 91 days advance purchase.

I could not generate a working link, but here is an example from LH.com

Flight on Friday, 07.07.2017 from Chicago to Munich

Departure time21:20 Departure airport
Chicago - O'Hare International, IL (ORD)
Arrival time13:05 +1 day Arrival airport
Munich - Franz Josef Strauss (MUC)
Cabin class
First (A)
Departure airplane numberLH flight LH435
Flight on Saturday, 08.07.2017 from Munich to Dublin

Departure time14:45 Departure airport
Munich - Franz Josef Strauss (MUC)
Arrival time16:10 Arrival airport
Dublin (DUB)
Cabin class
Business (J)
Departure airplane numberLH flight LH2520
Flight on Monday, 10.07.2017 from Dublin to Munich

Departure time17:05 Departure airport
Dublin (DUB)
Arrival time20:20 Arrival airport
Munich - Franz Josef Strauss (MUC)
Cabin class
Business (J)
Departure airplane numberLH flight LH2521
Flight on Sunday, 23.07.2017 from Munich to Chicago

Departure time15:40 Departure airport
Munich - Franz Josef Strauss (MUC)
Arrival time18:30 Arrival airport
Chicago - O'Hare International, IL (ORD)
Cabin class
First (A)
Departure airplane numberLH flight LH434
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incl. taxes and carrier imposed fees USD 4,468.01
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If I want to book this fare, I would have chosen the ORD-FRA flight with the superior first class product on the 748i @:-)