The group has been around since 2005 when they began as a duo--using live looping and improve. A couple of years later they added a saxophone, then later still a cellist and a violinist. The music is hard to nail down. They have ambient, classical, jazz and low-fi influences surely but hanging a genre on them isn't easy (nor productive). Their live show is worth a look. When someone writes "classical and jazz" that may make some people's eyes glaze over. Resist! A Light Sleeper are not defined by the bits and pieces of the genres they incorporate in their music.
Perhaps "orchestral" is a better word to use than "classical."