Judith Sole believed the resource was in decline, fishing quotas were not sustainable, and that the species was close to "commercial extinction", according to the report.
She reportedly lodged the application in the public interest in January and argued the matter herself, even though she is not a lawyer.
Sole told Judge Burton Fourie on Thursday that drastic action was needed in the form of a full suspension, or, alternatively, to allow only subsistence fishing but not commercial fishing.
Lawyers for the fisheries department questioned whether she had considered the socio-economic consequences of her request.
The West Coast Rock Lobster Association reportedly said that should a suspension be granted, it wanted a plan to be established to assist with subsidies.
Judgment is expected soon.