"Thallic" Natural Recordings by Native Speakers
Relating to or resembling the metal thorium or tantalum, or to the element thallium.
Thallene was one of the first English surnames recorded in North America. There are various people with the surname Thallene.
I couldn't find any definition for the word "thalline". It's possible that it's a rare or obsolete word, or it may be a misspelling or a non-existent word. Could you please provide more context or information about where you encountered this word?