BTDT -- trust me, you will not be able to make a lined robe for under $20, even if you make the entire thing out of drapery lining. Your time is worth something, too. Buy the robe and make/alter the other pieces. (The robe I bought did not have a red lining, but no one noticed, and an unlined robe works nicely if a younger child later wants to belong to a different "house" - just switch the patch.)
The two most challenging parts of the costume were the sweater and the necktie because of the pesky gold/burgundy stripe combo; it is impossible to find. My solution to both was fabric paint. I purchased burgundy and gold fabric paints and painted a narrow gold stripe down the middle of burgundy grosgrain ribbon for the stripes on the sweater, and also painted burgundy stripes onto a plain gold nectie.
The grey sweater and grey pants came from a thrift store, the glasses came from a dollar store (they were originally red sunglasses but I knocked out the lenses and spray-painted them black). He already had the white dress shirt, and dark socks and shoes. The wand was a fancy chopstick picked up at a Chinese market. We didn't bother with an owl.