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Hello ,
I'm not sure if I should say "at lightning speed" or "with lightning speed" in the following sentences, or if either way is grammatically correct.
1. The plane flew "with / at" lightning speed.
2. She talks "with / at" lightning speed.
3. China is developing "with / at" lightning speed.
4. He works "with / at" lightning speed.
Is there a grammar rule about using the word "with" or "at" when you are using it in combination with the expression "lightning speed"?

At a practical level, there seems hardly any difference in meaning between them (though doubtless some hefty monograph on prepositions would leave no stone unturned in saying otherwise). As for grammar rules, each appears perfectly grammatical.

Hello,
Thank you very much for taking the time to answer my question.
Best wishes

While both are grammatically correct, "at lightning speed" sounds better, as the preposition "at" collocates with "lightning speed" (they tend to occur together).

This collocation can be seen at work in "at breakneck speed" as well.

I want to thank you for taking the time to answer my question.