EDIT: TL;DR - Live TV not available on Roku - see bottom
EDIT1: App version 5.0.0 released, restores Live TV (for NFL Network)
You didnt mention your Roku model # or firmware version (Settings/System/About) or app version (highlight the app and press Options (*) on the remote).
I installed the NFL app and activated it, but I ran into several different odd issues (including activation issues) before it worked properly, and (non-Live TV) playback took about 30 seconds to start.
There is no "Live TV" option/tab, it just auto-plays available videos.
(As an aside, NFL.com is the worst performing/least optimized website I've ever encountered, and only CBS-affiliate sites give it a challenge as "slowest to load/render"..)
Reinstall the NFL app:
1) Remove the NFL app (Highlight the app, press the Options (*) button on the remote, then Remove)
2) RESTART the Roku (Settings/System/System restart/Restart) <-- MUST DO THIS HERE!!!
3) Re-install the NFL app
(Otherwise, if you dont restart settings/cached data associated with the app are left behind and it wont be a clean re-install)
If that doesnt work, you'll need to contact the NFL (they code and publish the app):
https://digitalcare.nfl.com/hc/en-us
EDIT: These 2 articles indicate it isnt available on Roku:
https://digitalcare.nfl.com/hc/en-us/articles/212046277-Live-Video-in-the-NFL-App
https://digitalcare.nfl.com/hc/en-us/articles/115015629547-Using-your-TV-Provider-account-to-watch-l...
