The Lottery helps in many ways but it really shouldn't effect the Rangers plans THAT much this off-season.
Shattenkirk should be moved if possible
Kreider should be moved if possible
At least one of Vesey/Namestnikov/Fast should be moved
The team has young players in Rykov, Hajek and Lindgren who will be pushing for spots on defense next year. There should be no less than 1 NHL top-6 spot available to start the season.
The team also has Kravtsov coming over and he should be in the NHL. Andersson, Chytil, Howden, Nieves all are NHL players. They need to make sure these guys have top-12 slots from Day 1. Kaako is another one if he is the selection.
If no one is traded:
Kreider-Zib-Kravtsov
Buch-Strome-Kaako
Lemieux-Chytil-Namestnikov
Andersson-Howden-Fast
Vesey
Nieves
Staal-DeAngelo
Skjei-Shattenkirk
Smith-Pionk
Hajek
Lindgren
Rykov
This doesn't even include anyone surprising like a Meskanen, Fontaine, Gettinger, Day or anyone else.
Gorton has his work cut out for him and he needs to move bodies for assets.
I will also say that considering the youth on this team I would be on the lookout to add another player or two who can both play the game and doesn't mind standing up for their teammates for the lower lines.