Only when the commodities are used in a high enough quantity is there enough incentive to really try to create as much of them as possible.
I don't think lobster is more scarce these days, than it was in the past. Rather the opposite.
Here is some index of north american lobster catch: http://www.asmfc.org/species/american-lobster
Looks as though it may have stalled a bit since 2015. But before that lobster catch definitely grew a lot.
Obviously with things like lobsters there'll be geographical variations, but I don't think there's any reason to suppose that lobsters have become a luxury good due to scarcity.
https://academic.oup.com/icesjms/article/72/suppl_1/i7/62044...
Evidence of lobster use comprises midden remains, artwork, artefacts, writings about lobsters, and written sources describing the fishing practices of indigenous peoples.
+1 for your paper.
Overlobstering is a despicable habit which should be stopped wherever it's happening.
It's just neither driving lobsters status as a luxury good, nor is it significantly affecting the amount of lobster.