I think he would be picked right around #20-#23 right now. No one in the Top 10 is not getting reselected by their teams just one year after the draft.
From 11-20:
11 Conor Geekie - Good year, Lambert not being selected over
12 Denton Mateychuk - Good year, Lambert not being selected over
13 Frank Nazar - Injured most of the year, but was top 10 talent without injuries. Chicago hangs onto him
14 Rutger McGroarty - Good year, Lambert not being selected over
15 Jonathan Lekkerimaki - Up and down year, but really turned it on in the playoffs. Kind of similar to Lambert. Maybe they go Lambert instead
16 Noah Ostlund - Good year, Lambert not being selected over
17 Joakim Kemell - Good year, Lambert not being selected over
18 Lian Bichsel - Good year, Lambert not being selected over
19 Liam Ohgren - Very good playoffs
20 Ivan Miroshnichenko - Rough year, could see Lambert here
So if only 1-3 guys are going out of the top 20, and then you have players like Kulich and Snuggerud from 21-30, I expect Lambert to climb up a bit, but not to top 15 type pick in a redraft.