That's the Conflict of Interest Act, yes.
With respect to the Lobbying Act, it applies to lobbyists who are required to register under the act, and the vast majority of them are private citizens. It also applies to organizations and corporations. Corporations effectively under the act are share capital corporations, and organizations include not-for-profit corporations and many other types of charities, unions, and other organizations like that.
Effectively, the answer to your question is yes, the Lobbying Act applies to the private sector and almost exclusively, although of course on the other side of the lobbying, there are public office holders because they are the ones who are being lobbied.