It is irrelevant that you are not on the lease.  You have a right to compensation for your injury because you slipped and fell on the premises.  Even if you were a visitor or trespasser, you would be entitled to compensation for your injury which occurred on the premises.Prior to filing a lawsuit based on premises liability, it may be possible to settle the case with the insurance carrier for the landlord. Obtain the name, address, and telephone number of the landlord's insurance carrier.  Notify the insurance carrier in writing that you will be filing a personal injury claim.When you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary which means having reached a point in your medical treatment where no further improvement is anticipated, obtain your medical bills, medical reports, and documentation of wage loss.  Your claim filed with the landlord's insurance carrier should include those items.Compensation for the medical bills is straight reimbursement.  The medical reports document your injury and are used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.If the case is settled with the landlord's insurance carrier, NO lawsuit is filed.If you are dissatisfied with settlement offers from the landlord's insurance carrier, reject the settlement offers and file a lawsuit based on premises liability against the landlord.If the case is NOT settled, your lawsuit against the landlord must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.