Common-law spouse LOC
A common-law spouse may work with LOC. The prospective employer downloads and completes the Letter of Consent (Common-Law Spouse) application form, then submits it and supporting documents online. This page describes an employer-applied route and does not state an independent self-employed-business route.
Other LTVP family members
Other holders first need a Singapore job offer, then the prospective employer applies for EP, S Pass or Work Permit. The holder must meet every criterion of the work pass selected. The LTVP alone is not work permission.
Official source
Written independently from official MOM source material.