First, congrats on the adoption.
I've met some really sweet examples of the brush-tongue birds.
I'm disappointed to hear you weren't informed of their extraordinary abilities of jet-propelled excretion.
It's very sad because I know for a fact that kind of omission has caused the rehoming of more than one Lori.
I'll be honest, as loving and funny as they are, it's one of the things that kept me from seriously looking at Lories & Lorikeets when my family was looking for a new feathered addition....
Yeah! They're poop squirters.......
.. gooey, poop squirters....
As for possible solutions to your problem, it depends how far ya want to go & how much $$ ya want to spend.
I think the most expensive way would be putting clear plastic panels on the outside of the bars. You need 3 sheets of 3/8" clear Acrylic or Lexan(sp?) long enough to cover the lower 3/4ths of the cage height & the stainless steel hardware (nuts, bolts & washers) to hold them on. You could use thinner plastic, but if the bird manages to get it's beak on those panels, they better be able to withstand some abuse.
The biggest drawback to this idea is that unless you use 4" bolts with spacers to give the panels some clearance from the bars, you're going to continuously need to remove the panels to clean them.
Though not as stylish as a hanging rug or even a blanket, plastic sheeting can be your friend. It's really easy to wipe clean & fairly cheap to replace.
Tape it to the walls behind & around the cage. You can even lay a sheet on the floor to catch all those "world record attempts" out into the room.
((Try to make sure your bird's cage &/or playstand are far enough away that the bird can't lean out & chew on the edges of the sheeting.))
You can buy it in large rolls of varying thicknesses, lengths and widths as "vapour barrier" from your local Home depot or similar store.
Having experience with using "flightsuits", I can tell you the diaper route will be OK for short periods, but completely impractical as a long term solution.
Our White Capped Pionus occasionally has looser droppings and I know the wetter the poops, the more often you are going to need to change the pad. With a Lorikeet, I'm pretty sure you would be changing the liner every 2 hours, three tops.
NOTE: If you do go to using a flightsuit at any time, do yourself a favour and install an extra leak shield layer.
Leak Shield:
Cut a small rounded "cone" (the same shape as the suits inner liner) from your plastic sheeting
and insert it inside the flightsuit between the liner and the outer material.
Hope that helps with your dilemma, and good luck with your FID!
BTW, any chances of posting some pics? We'd love to see your Lorikeet!