Pursuant to the Law on Lawyers, it seems that fully foreign-owned law firms established in Lao PDR are able to counsel on domestic law and represent clients on Laotian courts, as long as these activities are carried by a Laorian lawyer.
"Article 49.      Foreign Legal Enterprises
A foreign legal enterprise registered in the Lao PDR is entitled to provide consultancy/advice regarding foreign laws and international laws.
Foreign legal enterprises which have (a) Lao Lawyer(s) as joint investor(s) or employ Lao lawyers are entitled to provide consultancy/advice on Lao law and to litigate cases in the courts of the Lao PDR through such Lao Lawyer". (Law on Lawyers No. 010/NA, dated 21 December 2011, Art. 49)
Law on Lawyers No. 010/NA, dated 21 December 2011, Art. 49.
[<a href="http://laoservicesportal.org.la/images/download/Announcement_2017040402040726.pdf">Law</a>]