The link you shared says only in specific circumstances can someone opt out of LexusNexus:

Opting out of LexisNexis can be more complex than removing your data from other people-search sites. To have your information taken down, you must meet specific criteria, and LexisNexis may request additional documentation:

• Victim of identity theft: you need to provide a police report documenting the identity theft or similar documentation.

• Law enforcement officers or public officials facing threats of severe bodily harm or death:** **you must submit a letter from their supervisor confirming the nature of their position and the threats.

• At risk of physical harm but not in law enforcement: you’ll need to submit a protective order from the court, a police report, or similar documentation.