50 CFR 622.2
-
Caribbean spiny lobster means
Panulirus argus.
50
CFR 622.37(b)
– Minimum size 3.5 inches carapace length.
50 CFR
622.38(b)
- A Caribbean spiny lobster must be maintained with head
and carapace intact.
50 CFR 622.32(b)
(iii) -
Egg
-bearing spiny
lobster in the Caribbean EEZ must be returned to the water
unharmed. An egg
-bearing spiny lobster may be retained in a trap,
provided the trap is returned immediately to the water. An egg
-
bearing spiny lobster may not be stripped, scraped, shaved, clipped,
or in any other manner molested, in order to remove the eggs.
50
CFR 622.31(
j) - Spears and hooks. A spear, hook, or similar device
may not be used in the Caribbean EEZ to harvest a Caribbean spiny
lobster. The possession of a speared, pierced, or punctured
Caribbean spiny lobster in or from the Caribbean EEZ is prima
facie
evidence of violation of this section.

and I also found this about slipper lobsters:
Egg-bearing (berried) spiny lobster and ridged slipper lobster (also
commonly known as shovelnose or bulldozer lobster) must be released
unharmed. Stripping egg-bearing females of eggs, and
possession of spiny or ridged slipper lobster tails from which eggs have
been removed is prohibited. Eggs are an orange, yellow, brown, or red
mass found covering the underside of the lobster’s tail.
Gear such as spears, hooks, wire snares, and any device which could
puncture, penetrate, or crush the shell of the lobster is prohibited.