As I understand LH's current schedules they service CPT and JNB with separate direct, non-stop flights, which is good if you are going to CPT as you do not have to sit on the plane at JNB for a few hours. FRA-CPT is serviced with a 3-class A340-300 with eight first class seasts.

The OP should be able to get one award seat IAD-FRA-CPT in F on LH now as the 90-day 'window' on UA/MP-issued star alliance award travel on LH across the Atlantic has been lifted. This will cost 160,000 miles in FC. Lately it seems like LH has one FC award seat available at initial inventory allocation on A340's, and this is available to LH's own M&M flyers as well as Star Alliance partners, at least that's been my recent, anecdotal experience. Getting UA for the trans-Atlantic portion (i.e. Saver) will be challenging.