I think the issue you would face would be the agreement on internal trade. Assuming that the lobbyist registry only contains Canadian lobby firms or lobbyists who are Canadian, the issue, then, would be the agreement on internal trade. Again, for over $100,000 for services and over $25,000 for contracts, it requires the government to offer an open, competitive, fair bidding process.
The question would be: how could you offer an open, competitive, fair bidding process for some given service if you're going to discriminate against a class of firms because they conduct lobbying activities? That's where it creates the potential for this violation of the obligations on the government under the agreement on internal trade.