I would request to be let to use your laptop.

[tufguy]

1) I would request you to let me use your laptop.
2) I would request to be let to use your laptop.

Please check my second sentence. I want to write a passive sentence using "let".

 

[5jj]

I would request you to

That is very stiff. 'Please' is more natural.

2) I would request to be let to use your laptop.

That does not work at all. You can be permitted to do something, but not let to do it.

 

[tedmc]

Can I use your laptop, please?

Could you let me use your laptop, please?

Can I borrow your laptop (for a while), please?