N.M. Stat. § 48-3-9
[Loss of lien.]
Any lien acquired under the provisions of this law [48-3-1 to 48-3-15 NMSA 1978]
except those provided in Sections 48-3-5 and 48-3-7 NMSA 1978 hereof shall become
void, if the person entitled to the same shall consent that the property subject thereto be
removed from his control or possession, except as against the person at whose request
the repairs or parts were furnished and the labor performed. In the case of the liens
provided in Sections 48-3-5 and 48-3-7 NMSA 1978, if the person or persons entitled to
the lien consent to a removal of the property subject to the lien from the leased
premises the lien shall become void.