Named after the German-born Australian naturalist Baron Ferdinand Jacob Heinrich Müller (1825–1896), the species has been the subject of much morphological and nomenclature debate.

The head is elongated displaying a brown to black flecked pattern with recessed ears, and pointed snout providing evidence of adaptive fossorial behaviour.

Typically, individuals will begin the day in search of the sun to raise body temperatures to gain energy for foraging, and to aid with digestion.

Like most ectotherms, when energy levels are adequate, individuals will often seek shelter beneath sand, or in the form of loose soil, fallen logs, and the cover of ground litter and debris.

In the more arid parts of the continent, eggs are likely to be deposited under the protection of sand, providing potential offspring with the benefits of security and ideal climatic conditions for incubation.

Due to the size differences, females are likely to select in favour of larger surface dwelling invertebrates, as opposed to males who spend most of their time foraging for smaller more elusive prey.

[6] Similar to many other species of Scincidae, individuals have the inherent morphological trait of caudal autotomy allowing them to drop or lose part of their tails in the event of capture.

[9] As with many other species of animal on the Australian continent, impacts of land clearing, altered fire regimes, and agricultural endeavours result in loss of habitat for L. muelleri.