As a practical matter, you do not have recourse unless the lease (oral or written) under which you are leasing the premises gives you possession or use of the storage building; that is because it is legal for a landlord to only rent part of his land or space, or to hold back some land or space for himself, so there is no inherent right to have access to that storage building. If you have rented this space, though, you can make the landlord let you use it, which will also address the electrical issue.If  you don't have the right to that space, there really is nothing to be done. While the landlord should not be charging you for the electricity used in his space, unless under your lease, you agreed to pay for all power usage at the property, regardless of who controls certain space (it is legal for a tenant to agree to pay for more than his share), given how little the electricity consummed by five lights costs, you would spend more in terms of money and effort suing your landlord to recover the electrical costs then you would get back.