Lawgivers enforced the will of Landru when other measures, such as absorption, failed. Dressed in drab robes, they carried staves that could absorb and kill. Lawgivers existed in sufficient quantity that several could respond to any particular incident, and they were easily contacted by members of the population who needed them.
Spock, on examining the staff taken from a lawgiver by Kirk, noted that it appeared to be a hollow tube -- a weapon with no mechanism. He theorized that the staves were antennae that received some sort of broadcast power.
Kirk's experiences suggested that the lawgivers were under extremely deep control -- far deeper even than the control exercised over most of the populace. They were essentially incapable of independent thought, taking all of their direction and volition from Landru. Because of this, they were initially unable to handle disobedience. Betan society was based on absolute obedience to Landru or his representatives, and the breakdown of that left them confused. Landru quickly corrected this flaw; when subsequently presented with disobedience, they threatened death immediately.
Unlike most Betans, lawgivers could initate a conversation with Landru via the process of communing. While communing, there were in a trance-like state and largely unresponsive to external stimuli. They communed with Landru at regular intervals, and considered this a pleasurable experience. They also communed when exposed to stimuli outside of their experience, and required new instructions.
Lawgivers, as representatives of Landru, were viewed with quasi-mystical reverence by most citizens of Beta III. Many thought they were everywhere, all seeing and all knowing, but this was clearly not the case: they were unaware of specific members of the underground, or of the landing party, until Hacom contacted them.
During Kirk's discussion with Landru, the machine was forced to use all of its reasoning power to debate him; this caused several lawgivers to enter the Hall of Audiences in a panicked state, begging for guidance. (TOS: "The Return of the Archons")