I can provide a counter for each and every one of these claims that the results will be even worse.
1. They replaced a 0 sack guy in Hayden with a 1 sack guy in Thornton. To now expect a much improved pass rush based on that is wishful thinking and not based on supportable fact.
2. Lawrence is not only suspended for the first month of the season, but will now be the #1 focus of opposing defense because he's the only known threat the Cowboys have. Far less single blocking without Greg Hardy drawing the double teams in the other side. Given his back surgery, suspensions, and now being the focal point, I think it's more reasonable to expect a lower sack total than a higher one.
3. Another point based in assumption and wishful thinking. While I also hope that this becomes the case, until it doesn't, it simply isn't the case. If and when the Cowboys' offense is playing with a lead, it could certainly give an advantage to a pass rush, but only if the defensive players are then capable of doing their job.
The only fact is that a largely disappointing pass rush from 2015 has lost much more pass rush talent than it has gained and now we are left to hope that what they now do have can outperform expectations and past performance.