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Actually the parent wants me to straightforwardly lie to her kid and tell her that she passed an exam when she didn't.

That's appalling!!! How will they explain to the child the absence of a certificate? which I'm sure the child will know (or find out about) comes as part-and-parcel of an examination pass.
Like you, I think I would politely withdraw from teaching in this sort of scenario.
There is nothing wrong in failure, we all fail at something at some point in life - it's part of life - but we learn to deal with it, and often learn a lesson from it.....well sometimes! Protecting children from failure will do them more harm than good in the long run.
NB. I've heard that GCSE's will no longer be marked with any sort of fail - even if the student doesn't achieve the lowest grade. Apparently a 'Deferred Pass' (whatever that's supposed to mean) will be issued instead!!!
What sort of message is being sent to the younger generations by doing this??!!