Is it worth filing a lawsuit on my landlord for a sprained ankle?

Did your landlord put a banana peel on the staircase? Did your landlord pour a can of motor oil on the staircase? Did your landlord throw some shaved ice on the staircase? In other words, you have not explained how it was that landlord was the one that caused your mom to fall. Based on your story, your mom tripped for no other reason than because she was a klutz. That's not the landlord's fault. It appears your mom has no legal basis for a lawsuit based on the facts that you have presented.