It is possible to sue the landlord. The question is whether or not he had notice of the dangerous conditino and sufficient time to correct it. If the water was on the steps for quite some time and at an hour where there was a lot of foot traffic then you would be able to argue that he should have corrected the dangerous condition knowing the dangers it could create. Feel free to click on my profile as I have already written an article about what to do after you have suffered a slip and fall injury, or on the link below for more information.
