What @Bubbles14 Explained in his comment

My guess is the 0.06 second rule. Maybe Misa also wrote L's name in another Death Note at almost the exact same time as Light, so neither entry worked and L survived.

The 0.06-Second Rule: Simultaneous Entry

If the same person's name is written in two or more Death Notes within 0.06 seconds, the entries cancel each other out.
• The Result: The notebooks become invalid for that specific entry, and the targeted person will not die.
• The Exception: If the time gap is greater than 0.06 seconds, whichever notebook was written in first takes full priority, and the victim dies.

So since Light was under surveillance, L planned this strategy cuz he knew Light would write his name in the prison, so he kept Misa amane ready with her death note.

There is still one best explanation yet to be figured, You can also find more possible explanations, And yes you can use any source for reference, example using AI.

Is there any mastermind out there?