How long after you purchase a home can you file a lawsuit on the previous owner for lying about a leaky basement.

On what grounds do you have grounds for a law suit.

Was there a home inspection ?

Was there written statements about the basement leaking

Next when and where did it leak ( example here in Atlanta basements that never leaked did during the last winter floods

There is no way to answer this question without knowing what jurisdiction (i.e.: state, assuming you are in the U.S.) you are in.