It would be open now. The problem is that Thai Airways is not releasing award seats to partners (including lifemiles) until 14 days prior to departure. This means it's going to be hard to find seats out of Australia all the way to Europe. Air China might be your best bet.
Use the united Ailrines search engine to see what options they give you, then look for the matching award space on Lifemiles. You may be able to build your own itinerary.
You may be able to construct some flights. Using EVA Air out of BNE to TPE, then search from TPE Europe. Maybe United has some seats via USA.
you cannot book these things by phone. The ONLY time you can book by phone is if you can see the flights on line but you get an error when going to the passenger details or payment screens. Constructed routings are not available by phone, only by email
You may well find it's almost as cheap to buy a revenue ticket these days on the likes of Hainan Airlines ($3500 return BNE-BRU), or Vietnam Airlines (for around $4000) than bother with Lifemiles.