The answer is
All's Well That Ends Well, a famous Shakespeare play.
My first is found in Aquaman's new super-secret lair.
This is an amusing reference to Aquaman's Revenge!, in which one of your possessions is an awl.
My second is a prison where a climbing snail's ensnared.
This is a reference to https://puzzling.stackexchange.com/questions/248/how-long-does-it-take-for-the-snail-to-get-out-of-the-well. In the problem, the snail is trapped in a well.
My third, repeated seven times, requires punctuation.
This is a reference to A grammatically valid sentence in English containing seven "that"'s in a row?. The word in question is that.
My fourth comprises eight furlongs; embodies termination.
This refers to Quite a distance from the start to the end of this short riddle. Who am I?. The word in question is ends. It certainly does embody termination, as termination is the end of something.
My fifth must be connected to three homes with expertise.
This is a cute reference to Connect 3 houses with 3 wells, in which three houses must be connected to three wells without the pipes crossing.