He joined the Danish Foreign Ministry in 1984. In the period 1994–1998 he served as deputy leader of the Danish embassy in Pretoria, South Africa. He was deputy leader of the Foreign Ministry's Department for Asian affairs 1998–2000 before heading the Ministry's Department for Middle East and Latin-American affairs 2000–2003. When leading the Middle East Department Denmark held the presidency of the Council of the EU July–December 2002 and Faaborg-Andersen co-authored the Road map for peace.
In the period 2003–2008, Faaborg-Andersen was Denmark's deputy permanent representative to the United Nations in New York and in the period 2005–2006 also to the Security Council. He went on to serve as Danish ambassador to the Political and Security Committee of EU in Brussels in 2008 and held the position until he in 2013 was appointed ambassador to Israel for the EU by Catherine Ashton.
- Dansk diplomat i spidsen for EU i Israel (in Danish) Globalnyt.dk. (Archived at WebCite).
- Akiva Eldar (23 December 2013) Europe threatens to put pressure on settlements with product labeling Al-Monitor.
- Lars Faaborg-Andersen som ny chef for EU's delegation i Tel Aviv (in Danish) Politiken.
- Nir Levitan (9 May 2016) DENMARK IN THE MIDDLE EASTThe Jerusalem Post