The best replacement for lx7 is rx100.

The best alternatives to lx7 are rated as following:
★★★★★  rx100
★★★  s110
★★★  g15
★★★  lx5
★★★  lf1
★★  x20
★★  s120
★★  g16
★★  xz-2
★  rx100 ii
★  lx7k
★  gx1
★  gm1
★  canon s100
★  zs30
★  x10
★  sony rx100
★  lx3
★  canon g15
★  mx1
★  hx50v
  s100
  olympus xz2
  tz40
  xz2
  p330
  pentax q

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Speaking about lx7, one probably shouldn't forget about rx100.

Other search terms related to lx7 and their ratings are:
★★★★★ rx100
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Google Trends

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lx7
rx100
s110