Thanks for posting Paragraph 14 from your lease. It's quite different from the "Use of Premises" paragraph in our own lease, which was based on a common template from the early 1980s (possibly the same one used by Steve Rosenstein's co-op, to judge from the discussion above). You should check with an attorney to be sure, but it certainly appears that your board could not prohibit home occupations via a house rule with that language in your lease.

For comparison, here is our Paragraph 14 in its entirety:

"14. Use of Premises: The Lessee shall not, without the prior written consent of the Lessor on such conditions as Lessor may prescribe, occupy or use the apartment or permit the same or any part thereof to be occupied or used for any purpose other than as a private dwelling of the Lessee and Lessee's spouse, their children, grandchildren, parents, grandparents, brothers and sisters and domestic employees, and in no event shall more than one married couple occupy the apartment without the prior written consent of the Lessor. In addition to the foregoing, the apartment may be occupied from time to time by guests of the Lessee for a period of time not exceeding one month, unless a longer period is approved prior thereto in writing by the Lessor, but no guests may occupy the apartment unless one or more of the permitted adult residents are then in occupancy or unless consented to in writing prior thereto by the Lessor."