Isomerisation of alkanes under Lewis acidic conditions
The mechanism for butane is shown here, instead of a general n-alkane.

Initiation



As the comments have mentioned,  it probably begins by the protonation of butene impurities.

The Lewis acid, $\ce{AlCl3}$, stabilizes the chloride ion from $\ce{HCl}$ when the $\ce{H}$ is used to protonate the butene.

A secondary carbocation is formed, which undergoes methyl shift to form a primary carbocation. I have no idea why a primary carbocation can be formed.

Propagation



An alkane attacks the carbocation, and supplies a "hydride" to the carbocation to complete the carbocation.

Meanwhile, another carbocation is formed which also undergoes methyl shift to regenerate the carbocation at the beginning of this step.

Termination



I am going out of my way here to suggest a isobutyl chloride (1-chloro-2-methylpropane) termination product. I can't find other Lewis bases to complete the carbocation for the termination step.