With regards to the adoption in 1930: Legal adoptions in Qld began in 1928, according to this web-site.
http://artsonline.monash.edu.au/historyofadoption/queensland-adoption-records/Others with a better knowledge of Qld records may be able to tell you whether records are available which may give you more information.
Unfortunately open indexes for births in Qld only go up to 1918 so we can't search for a record which may be Elizabeth b1924.
The birth registration found by cupoflife in 1905 (Mary Elizabeth Donnelly) seems a possibility for Lilian Mary.
Edit: I note that Norah Valentine DONNELLY's husband, William PICKING died in 1935 and I think she remarried to a BURTON.
See below where I post:
I see a Norah Valentine BURTON on electoral rolls in Rockhampton but when I look harder they go up to 1980 and Norah Valentine DONNELLY/PICKING died in 1965.
Sorry!Not very helpful, I'm afraid!
Judith