It seems the [VERMIN_NOFISH] tag prevents them from being caught with the fishing labor.
Though I read there were some problems with lobsters giving off shells and with shell crafts.
I'd planned to create a giant lobster creature that would give off a giant shell material, is there any problems there?
Cave lobsters do give off shells as of v31.08, but the dwarves don't recognize them as shells and give you a "needs unrotten shell item" message when you try to make something with them. I don't know if they work for strange moods.
The problem is that the shells are made of CHITIN instead of SHELL. It's definitely possible to change their material, here's how:
1) Open b_detail_plan_default and find [BODY_DETAIL_PLAN:EXOSKELETON_TISSUE_LAYERS]. Look about 20 lines under that for [BP_LAYERS:BY_CATEGORY:SHELL:ARG1:100]. Change that to [BP_LAYERS:BY_CATEGORY:SHELL:SHELL:100].
2) Add the tags [USE_MATERIAL_TEMPLATE:SHELL:SHELL_TEMPLATE] and [USE_TISSUE_TEMPLATE:SHELL:SHELL_TEMPLATE] to the cave lobster raw, and your giant lobster raw if you make them.
However, I can tell you from personal experience that shell crafts are still bugged in this version, and no amount of modding will change that. Toady will get around to fixing it eventually, I'm sure. In the meantime, at least your lobsters can be useful for strange moods.