The lake atop the mountain has always been the lyre for intrepid hikers.

A 'lyre' is a stringed musical instrument, which does not contextually fit a lake attracting hikers. The word needed is one that means something which tempts or attracts. 'Lure' means something that tempts or is used to tempt a person or animal to do something, fitting perfectly with intrepid hikers being attracted to the mountain lake. The other options—link, line, life—do not capture the sense of attraction or temptation. Hence, 'lure' is the correct improvement.