She is both loyal and cruel, and neither.
On the one hand, she seeks advancement for her husband and appears prepared to do whatever it takes to achieve that, even to the point of killing her King--loyal and cruel.
Is she loyal? She does not betray Macbeth, nor does she abandon him. From our perspective, she is loyal, but I wonder whether an Elizabethan audience would agree (think Great Chain of Being). She is merciless in manipulating her "lord" Macbeth, even to the point where she argues that he is faithless if he breaks his promise to her and doesn't kill the king. A wife is supposed to obey her husband, but a (naturally superior)husband is not obliged to obey his wife. Her willingness to breach the natural order (killing the king and challenging her husband) suggests a flaw in her loyalty.
She certainly claims she is loyal when she says that she would rather tear her baby from her breast and dash its brains out than break a promise to her husband. Yet the real Lady Macbeth is less brave than she pretends to be. Dash her baby's brains out? She can't even kill Duncan because he reminds her too much of her father.
She talks cruel, but is she as mean as she says she is? I don't think so. She chides Macbeth for his weakness, yet she is the one who feels the deepest guilt, and as the play progresses,she tells him to stop. A truly cruel woman would enjoy inflicting pain and feel no remorse. Instead, the guilt she feels disrupts her sleep and eventually destroys her.
Loyalty and cruelty are not mutually exclusive. Lady Macbeth certainly is loyal to her treacherous husband. It is she who proposes to lure Duncan into their trap. See Act 1.6.59-70. Here, Macbeth and Lady Macbeth discuss the best way to trick Duncan. She tells her husband that his face is too easily read: Your face, my thane, is a book where men/May read strange matters (60-61)/Only look up clear./To alter favor ever is to fear./Leave the rest to me.
Lady Macbeth's cruelty lies in her ability to smile and betray simulateosuly.