No. A landlord is not obligated to paint between tenants.
The landlord is obligated, under the Minimum Housing and Health Standards, to ensure that walls and ceilings are in good repair, with no cracks or holes and that they are easy to clean. In the bathroom, the walls must be smooth and non-absorbent. In the kitchen, the walls have to be in very good condition to ensure that bacteria and pests do not become a problem. These requirements mean that while a landlord does not have to paint between every tenant, the landlord does have to ensure that painting is done on a regular basis to meet health standards.