Originally Posted by Recyclops

The challenge is that in addition to satisfying all of those rules, you need to find availability in the "A" fare bucket. Because of the connecting flights you also run into issues with "married segments", which means that even if, for example, there is availability in A for a particular flight ORD-FRA and for FRA-LHR, LH might still not be willing to sell that as a single ticket ORD-FRA-LHR in A.

There's really no good way to figure this out online. On LH's website the best you can do is try various dates to see if you can find some that work. Sites like ExpertFlyer that let you search for availability in specific fare buckets are better, but even this won't guarantee you a successful result because of the married segment issue. Your best bet is likely to work with a travel agent since they will be plugged directly into the GDS (e.g. Amadeus) and have much more powerful tools for searching for availability for specific fares.