This is how I understand the situation... and it's not about tourist dollars. If I am wrong I would be happy to hear the correct version!
Very sensibly all spear fishing for any species is banned under congressional law in Honduras. Spear fishing tends to be very selective and takes the biggest strongest healthiest members of a population and as such can be incredibly destructive.
To be able to legally spear even lion fish the NGOs that have got involved like Roatan Marine Park, Utila Center for Marine Ecology and Bay Islands Conservation Association had to petition central government HQ to make a special exemption in the law for spearing lion fish.
This has been granted on condition that spears are limited in design to what is needed to spear a lion fish and are licensed and have the license ID number engraved on them. Owners of the licensed spear are photographed and identification details are taken. The owners are responsible for the spears not ending up in the hands of disreputable spear fisherman, etc. Each spear can be tracked back to someone who purchased the license.
Personally, I much prefer controlled use of spears than a spear free for all which is probably (sooner or later) going to result in other species being taken and also a large amount of coral damage from clumsy/unskillful use of spears. Yes it is possible to take more lion fish. Will that actually make a big difference? That's up for debate...