Generally the lease requires you to hand back the property in the state you received it. This gives legal ownership of the items for insurance purposes and therefore it can be covered, however not all leases have this clause and if not then the tenant has no legal entitlement to claim for the items as he has no legal interest in them.
It is important that you take out adequate cover to match the requirements of the lease. You can be legally required to cover the building but if you dont take out the cover a standard shop policy will not include for it as it will simply cover tenant improvements, tenant contents etc but nothing owned by the landlord.