Lift is Strange is one of those games that is undeniably brilliant, but you have to know what you're in for. It's not actually what I would a "game", I would describe it as an interactive narrative. There're some aspects of exploration and problem solving, but it's mostly guiding the character through a scripted story with choices to make that affect where the story goes. I won't spoil anything, but it's a superb story. I definitely prefer the first LIS over the prequel BTS for reasons that I can't really explain without spoiling them, but it's up to you in the end how you feel.
If you bought the games on disk, the'll be complete, so don't worry.