I let him go, without hesitation.
My Geralt fully understood what kind of influence Letho had had and actually made on the different events in the North, but I felt no grudge, nor revenge for Letho. His intentions and his agenda weren't evil, his goal was always to ensure the rebuildment of the Witchers of the Viper school. He didn't have an idealistic view on the world, but rather a realistic one. While Geralt simply accepts that Witchers are relics, and will eventually 'go exctinct', Letho actually accepts what the world has come to, and actively wants to make a change on that. I doubt he cares who is the ruler, or who is the winner in the upcoming war. He simply has his own goals that he pursues and wants to achieve, and will take down almost anyone and 'aid' anyone if it strenghtens his goals, to some extent. My Geralt respected what Letho motives were, and while I may not have approved of Letho's so called "interference" on the stability of the North, his involvement could have ultimately made --as Geralt himself states-- the North even stronger and more united than ever (though it depends a large part on the different choices made in the game, and a lot if it is actually up to speculations in the end).
Another part to why I let him go is that I feel a certain amount of respect for him, and I believe Letho does this as well to Geralt. This can easily be seen when Letho offers Geralt Vodka which, if chosen, Geralt drinks from. Letho is certainly very ruthless, but he is also reasonable and compassionate. He did spare Geralt's life in Act 1, he (depending on choices made) saved Triss, and even throughout the dialogs you have with him, he took care of Yennefer when Geralt wasn't around. There's a lot more to Letho than meets the eye, and that makes him lot more interesting.
And as Geralt states himself, killing Letho will make no difference. The damage had been done, and Geralt had "cleared" his name to some extent. His death would've achieved nothing, if not only for stopping him for doing anything else in the future, which I doubt he will, if not blackmailed or anything between.
But truth be told, him being such a great antagonist also played a big role why I ultimately decided to let him go. And I'm as well interested to see what the future holds for him.