The "law startup" space is pretty active, but I think it helps to break things down a bit. Most probably would fit into one of these categories:
(1) Startups that aim for the consumer market by replacing lawyers in some way (e.g., LegalZoom, Shake, or other document automation software companies)
(2) Startups that aim for the consumer market by connecting people with lawyers (e.g., Priori Legal)
(3) Startups that aim for the legal support/services market by offering cheaper/better alternatives to existing software offerings (e.g., Ravel Law for legal research or Clio for practice management)
(4) Startups that aim for the legal support/services market by innovating in areas that traditionally have been inefficient and/or paper-intensive (e.g., Lex Machina for IP analytics or eDepoze for depositions)
(1) Startups that aim for the consumer market by replacing lawyers in some way (e.g., LegalZoom, Shake, or other document automation software companies) (2) Startups that aim for the consumer market by connecting people with lawyers (e.g., Priori Legal) (3) Startups that aim for the legal support/services market by offering cheaper/better alternatives to existing software offerings (e.g., Ravel Law for legal research or Clio for practice management) (4) Startups that aim for the legal support/services market by innovating in areas that traditionally have been inefficient and/or paper-intensive (e.g., Lex Machina for IP analytics or eDepoze for depositions)