Conaway graduated from Minor High School in 1978 and earned his bachelor of science at Athens State College in 1984. He went on to earn a masters in business administration at UAB in 1994 and an MA from Birmingham Theological Seminary in 2008.
He worked for several years in Huntsville before joining the Department of Veterans Affairs. He held several positions at the Birmingham VA Medical Center before resigning to join the staff of Guiding Light Church.
Conaway is also active in community service. He has worked as a chaplain at Cornerstone Christian School, a volunteer and board member of First Priority, an Equal Employment Opportunity Counselor at the Birmingham VA Medical Center, and as a volunteer and leader with numerous organizations, including Jimmie Hale Mission, Jefferson County Family Court Adolescent Mentoring Program, Christians Concerned for Prisoners, and the Institute for Youth Development.
He founded Charity in Action which offers GED prep, job prep, tutoring, parenting classes, financial literacy, and seminars for seniors, adults, and youths. He is a graduate of the 2007 class of Leadership Birmingham, vice chairman of the Neighborhood Housing Services of Birmingham, a former leader in Yes We Can! Birmingham, and former chairman of Birmingham Education Foundation.
Conaway ran as a candidate for Birmingham City Council District 2 in the 2009 Birmingham City Council election. For his platform, he pledged to forge partnerships with private-sector organizations to support parents and families, to build a coalition of leaders to assist in youth development, and to work with organizations working on community revitalization and economic development issues. He came in fourth in the election. He qualified again for the same seat in the 2017 Birmingham municipal election.
Conaway and his wife, Madeline, together have five children and four grandchildren.
- "Birmingham City Council elections: District 2 candidate Lawrence Conaway." (August 12, 2009) The Birmingham News