Question

It hasn’t been revealed yet

Oh alright! Thank you!

Because I had many premises in my head about why the Duke behaved the way he did. Saying, 'Leave him be"

Theory 1 :
Duke knows that Lin can protect himself. So leaves him be.

Theory 2 :
Duke wants to protect Lin. And doesn't want anybody else know how important Lin is. Therefore doesn't save him. (But this theory is false because everyone can openly see Duke adores him)

Theory 3 :
He send a tip off to the guards, and protected Lin indirectly.

I keep thinking it's important that Duke be the one save Lin, in the end.
He even said to the Marquis in quite a possessive tone that the most he can take is a few sips of tea. And Marquis challenged Duke directly by taking Lin.

Also and another theory could be that Euthigen saved Lin. He definitely has the power to poisen and give a rip-off about the Marquis.
And Euthigen usually does sneaky tip-offs anyway (evident from what we saw of Lin's first mission). But don't know what could be his motive to kill Marquis.
Where as the Duke definitely has a motive to poison Marquis. (Marquis knew about Duke's "other face")

But overall, I just personally wanted to see Lin protect herself

I think the duke genuinely meant what he said when he said let her be but maybe theres a small chance he wanted to save her

I think so as well. I saw the raws and what I got from it, is that it’s just part of who he is.

Yes, I hope so!

Ah yes, could be. I saw the raws as well, and he later does go to great lengths to save Lin, several times...

I actually think it was the guard woman who took pity on her and tipped off the guards

Oh yeah, that could be a possibility as well!!