Located only one attorney Rice from the north in Little Rock - so initials recorded here are wrong or her memory was bad:

Name: Milton L Rice
Age in 1870: 44
Estimated Birth Year: 1825
Birthplace: New York
Home in 1870: Little Rock, Pulaski, Arkansas
Race: White
Gender: Male
Value of real estate: View Image
Post Office: Little Rock
Roll: M593_62
Page: 250
Image: 498
Year: 1870

I came across this page during a Google search, and thought I'd contribute even though it's been years since the original posting. Milton Lycurgus Rice is my ancestor and I believe the lawyer you were looking for is his brother, Benjamin Franklin Rice. He lived in Little Rock from 1864-1875, according to this website: http://bioguide.congress.gov/scripts/biodisplay.pl?index=R000195