Which provision states that the insurer must defend all lawsuits against the insured?

The correct choice is related to the provision that specifies the insurer's duty to defend policyholders against lawsuits. Liability coverage is designed to protect insured parties from claims made by third parties for bodily injury or property damage. An essential component of this coverage is the insurer's obligation to provide a legal defense if a lawsuit is filed against the insured for incidents allegedly covered under the policy.

Liability coverage typically includes not just payment for damages that the insured may be found liable for, but foremost, it encompasses the insurer's promise to defend the insured in court, regardless of whether the claims are ultimately deemed valid. This aspect serves to protect the policyholder from the significant costs associated with legal defenses, which can arise even from unfounded or frivolous lawsuits.

The other options, while they sound plausible, do not generally capture the comprehensive nature of the insurer's obligation to defend. The defense clause, while it might imply a similar meaning, is not a widely recognized term in the context of insurance policies. Coverage extension and lawsuit assurance do not specifically refer to the insurer’s obligation to defend against lawsuits in the way liability coverage does. Thus, liability coverage appropriately reflects the legal requirement placed on insurers within most property and casualty insurance policies.