Can Lawyers use cloud services?

As usual, it depends. but with due diligence, yes.

The American Bar Association says yes. Specifically lawyers are obliged to keep informed about technology changes and to make reasonable efforts to protect client information.

22 state bar associations have published opinions that accept use of cloud services:
Alabama (Formal Opinion No. 2012-184), Alaska (Ethics Opinion No. 2014-3), Arizona (Opinion 09-04), California (Opinion 2010-179), Florida (Proposed Advisory Opinion 12-3), Illinois (Opinion No. 16-06), Iowa (Opinion 11-01), Maine (Opinion 194, Opinion 207), Massachusetts (Opinion 12-03), New Hampshire (Opinion 2012-13/4), New Jersey (Opinion 701), Nevada (Opinion 33), North Carolina (2011 Formal Ethics Opinion 6), Ohio (Informal Opinion 2013-03), Oregon (Opinion 2011-188), Pennsylvania (Opinion 2011-200), Tennessee (Formal Ethics Opinion 2015-F-159), Texas (Formal Ethics Opinion 680), Vermont (Opinion 2010-6), Virginia (Legal Ethics Opinion 1872), Washington (Advisory Opinion 2215), and Wisconsin (Formal Ethics Opinion EF-15-01). Source

A summary of those opinions is that lawyers may use cloud services if they take reasonable efforts to:

  1. prevent inadvertent or unauthorized access to that information

  2. maintain the confidentiality of the information

  3. establish reasonable safeguards to ensure the information is protected from loss, breaches, business interruptions, and other risks created by advancements in technology