Am unfamiliar with the permitted mileage restrictions. But even if I could get the PEK-FRA-EZE in LH F I would be very happy with that!
For certain tickets and routings airlines will impose a maximum number of miles you can fly to achieve that route. If say the distance between A and B is 5000 miles, they may allow a combination of flights up to that 5000 miles,
plus a leeway on top of that (usually 25%). So you could fly 6250 miles in this example. The 5000 miles is measured by the direct routing (great circle mapper is a good way to start this).
BNE-EZE comes in at 6870 base miles, so a rough and ready calculation of MPM might be ~8500 miles. (But this isn't always precise, the MPM will be calculated in the system). BNE-PEK-FRA-EZE comes in at 17000 miles, well in excess of the 6870.
PEK-EZE is 11900 miles, and via FRA is going to be withing the MPM. As would going the other way, via LAX for example.
PEK-FRA-EZE should be doable via the screenshot method. I know LM allows routings from at least as far as Chicago to Asia via Europe (although it's not offered on line).
You can always try the screenshot method from Australia, but it's likely they'd come back with an alternative in business class with AU-USA in business (if they can find it). In the meantime you might lose your F class on the PEK-FRA-EZE flights.
Just note that some of the LH F seating might not actually be bookable. If there are 2 (or more) seats showing for the LH flights you should be ok. If there's only one seat showing it might (in some cases) not actually be available to LM.