The Spiny Blue Lobster gets to be 12” and a 45 gal isn’t large enough IMO. The tank is only 3-4 months old and personally I think you are rushing just a tad to quickly to get this tank stocked. Tanks take awhile to stabilize and build up bacteria to support your bio load and even with good water parameters they can crash quickly.
What are your current water parameters, specifically nh3/no2/no3/alk/ph/sg/temp? Readings and test brands please, not just a reply they are “perfect”
Has copper ever been used on the main tank? How were your shrimp/lobster acclimated and when did you add them? Do you have a qt tank you can transport them to?
If they are damaged to the point of not being able to move at all there is little you can do for them.