Tenant improvements to apartment are tax deductible?

Sure, that’d work – provided the employer can document the rental payments under 280A. Even still, the owner has to report all the rental income.

The tenant is the lessee - no deduction unless business purpose

The landlord is the lessor - deduction allowed

What if the tenant sublets the apartment? Then the tenant becomes a lessor as well, so report the rent income and corresponding expenses including depreciation.