Text (SH+errata): 1/3. ; Whenever ~this~ deals damage to a creature, destroy that creature at end of combat. [Oracle 1999/05/01]
If it damages a creature outside of combat, its effect will destroy the creature at the end of the next combat. [Duelist Magazine #25, Page 31]
If a creature leaves play (including phasing out) before the end of combat, then the Lowland Basilisk effect on it will end. [Duelist Magazine #25, Page 31]