I did the same with the first (well, let's say reboot) episode. Sadly I couldn't 100% the whole game on Steam (only the single player part of it) because the multiplayer is dead nowadays. I still have to play RotR, when I find some time for it because Tomb Raider (2013) was a blast. :)
About the sequel: I hope we can see a trailer of the 3rd episode (Shadow of the Tomb Raider) during the E3 in June!
The last game I've finished, where reading everything was crucial in my opinion, is Quantum Break. It's one of the best time travel stories I've ever seen, but probably most people just ran/shoot through it without paying attention to the details. I think this partly explains the mixed reviews.