applying h1 if l1 expires by sept 24

Is it possible to apply h1 if l1 is expiring on sept 24?

or 



we can't apply for H1B if the l1 visa validity is not until oct 1.



We are trying to file h1b from a desi consultancy which is in USA and he says that he cant file for h1 as l1 is expiring in september