I'm sort of curious how much time Nintendo has to add to directs in months after certain events, like E3. 

For example, if Nintendo noticed certain reactions to their E3 conference, how much time past that do they need to specifically add something to address it. In time for a July Direct? August? September?

There was one time Nintendo did in a direct in july,but usually they wait until september after E3 to do a general direct and do a bunch of mini-directs and game specific ones in between.

Possible a splatoon direct this month for the DLC.

They do directs when they want events don't factor into their decisions as they already have a schedule in mind long before them.

Right and wrong. They do directs when they want, but you can bet that if there was some huge outcry over something and a direct could fix their public image, they would do so. Hell, there is some people that might argue they had a direct earlier this year that they did solely in response to rumors of a direct being so strong that they almost needed to have a direct or it would hurt their image if they didn't.

As for the OP. They could decide on a direct tomorrow and make it today. There isn't some insane production value in a direct that they would need weeks or months of advance prep time to make one.

I disagree Nintendo have never been phased by online reception even if they're aware of it simply because it's much better to stick to solid schedule then have knee jerk reactions that throw you off your game plan. I'd bet you they already know what they'll show in their next ND and knew before E3 even started, it's a form of guerrilla marketing and it works best in periods when things quiet down hence why January and September have often had NDs.

The octo expansion was released during E3, right after the championship finals.

Nintendo Directs generally release every 3 - 4 months, with some noticeable trends. there is usually a Direct at the end of the year, (late October, early November) and they have done a few on April 1st.

but thats a bit of a weird question since they dont usually address games in terms of media attention or controversy, even the likes of Federation Force or Animal Crossing: Amiibo Festival. if they have something new to show off, and it will release within the next year, they will show it in a Nintendo Direct. i suppose if they had to, it would be at the top of their list when scripting the direct, but it wouldnt really be given any more dedicated time than any other game being showed off when making the video

Oh wow really? Was a stealth release =p.

Hope this helps:

* Nintendo Switch Presentation Nintendo Switch hardware and games January 12, 2017
* Arms, Splatoon 2; and Nintendo Switch and Nintendo 3DS games April 12, 2017
* Nintendo Switch games June 13, 2017
* Nintendo Switch and Nintendo 3DS games September 13, 2017
* Nintendo Switch and Nintendo 3DS games, with a focus on Mario Tennis Aces for Nintendo Switch March 8, 2018
* Nintendo Switch games, with a focus on Super Smash Bros. Ultimate June 12, 2018