Question

what is meant by "not that the lust to kill had suddenly descended on her"
explain these lines.
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Answer 1

heya!!!!Good morning.

the sentence is said by narrator which meant that it was not that Mrs.packletide had suddenly decided to kill a tiger.

Answer 2

These lines mean that it wasn't a sudden desire to kill an animal that made Mrs Packeltide want to shoot a tiger.

She shot  the tiger because she wanted to outshine Loona Bimberton; not because she had a desire to kill a tiger.

 "Lust to kill" means a desire to kill. 

Mrs Packletide didn't have any innate desire to kill a tiger. It was just for the purpose of showing off that if Mrs Bimberton could shoot a tiger, so could she.