Personality:
Lamatsu's motive is, oversimplified, survival of the fittest—she believes that people who are not strong enough to face their fears must either become stronger or be destroyed. If they are not strong enough to defeat the enemies she throws against them, it's their fault, not hers. This doesn't mean that she's good at heart or seeking a peaceful, happy world—she is doing what she believes to be best, but she knows it's not really the "good" thing. However, she's not particularly fond of humanity, so her conscience doesn't get in her way.
There are only two people in the world that she loves, her mother Katasu and her adopted son Thasen. She respects Marduk and his other Acolytes, but she doesn't really love them. If she had to choose between her mother and Thasen and Marduk, she'd choose her mother and Thasen. Marduk has seen to it that no such conflict of interest shall occur—Thasen owes his health to Marduk's power, and Marduk also provides for Katasu's well being.
Tsuraine inherited some magic power from her mother and the physical strength of her father, who, she is reasonably certain, was one of the Earthbound Ones. She doesn't possess the physical weakness of the Atlanteans, nor must she rely solely on her mundane strength to survive. In addition to the powers that Marduk gave her, she's pretty powerful all-around, and that's probably why she's near the top of the power structure in the Brotherhood of Redemption. She's not invincible, but she certainly makes a formidable enemy. However, despite her Earthbound heritage, she could not inherit the resistance and endurance that comes from a lifetime of hard work—though her constant travel of the past few years has toughened her, she still doesn't have the strength of one born on the surface. Also, any low-ranking Atlantean could beat her in a contest of magic—without the assistance in power given to her by Marduk, anyway.
If you want to defeat her, the best way to go about it is probably to go after Thasen or Katasu—her mother and son are her weaknesses, and she would be willing to concede defeat to protect them. She wouldn't give up immediately, but she would rather lose a battle than endanger their lives. However, Thasen isn't just a liability—although she wouldn't use him as a shield, she knows that people are less likely to distrust, dislike, or attack a woman with a six-year-old child in tow.
The face she shows to the world is that of the Priestess Tsuraine, a benevolent lady dressed in white with Thasen (small child = sympathy bait) always at her side. She holds the lantern in her other hand, and it emits a soft, comforting light as it absorbs the fear of those around her. She smiles kindly, heals, and preaches the gospel of Marduk. However, the teaching of disciples is not her job—she is only a traveling preacher, and sends the converts she makes to others for teaching/indoctrination. The benevolent Priestess Tsuraine is not connected with the red-garbed Lamatsu, and that's just the way she likes it. Before the senshi show up, Tsuraine doesn't show her Lamatsu form at all—she does institute disasters and monsters, but it's all done behind the scenes.
Pros/Strengths:
More physical strength than an Atlantean, more magical power than an Earthbound One.
Higher resistance to both physical and magical attacks
Good at feigning innocence/benevolence
Thasen = sympathy bait (you wouldn't want to hurt an innocent six year old, would you?)
Cons/Weaknesses:
Best way to defeat Lamatsu: take Thasen or Katasu hostage
Not as strong as a "true" Earthbound One nor as magically gifted as a good Atlantean