How can King Lear be understood as a morality play?

A morality play offers moral lessons about good and evil, with the characters representing different virtues and vices.
In King Lear, the main characters likewise represents different virtues and vices. Cordelia, for example, represents the virtues of loyalty and filial love for her father, as well as the virtue of honesty: unlike her sisters, she refuses to exaggerate her love for Lear.
In opposition to Cordelia, her older sisters Goneril and Regan represent the vices of disloyalty, dishonesty, disrespect of a parent, and treachery. They will lavish any praise on their father to get what they want, which is his kingdom and the power it offers them. They lie when they claim great and undying love for Lear, for as soon as they are able, they rob him of his dignity and finally cast him into a cold storm as if he is so much refuse.
The Fool, ironically, represents the virtue of wisdom: from the start he knows Lear is making a huge mistake in giving away his power and trusting the words people say. Lear, on the other hand, represents the vice of foolishness for being unable to distinguish between words and deeds and discern who truly loves him.
As you read the play, you will find more of these oppositions between virtue and vice in the various characters.

There are many features of William Shakespeare’s King Lear that are reminiscent of the morality play, a genre of Medieval theatre. Morality plays are allegories in which the main player meets personified symbols of various virtues and faults. It is heavily drawn from earlier dramas. It is clear from the references in this play that Shakespeare was very familiar with morality drama.
King Lear features a powerful king figure and powers of good and evil. While the deep structure of other Shakespeare plays like Othello are based on the morality play, it only comprises the bare outline. King Lear, however, is full of details that suggest the morality play as well. For instance, the morality play often depicted scenes of “comic depravity” that alternated with scenes of “tragic seriousness." This is clear in the comic elements of the King Lear tragedy. The presence of an “all-licensed fool” in the tragedy is an interesting comedic element (Act 1, Scene 4, Line 198). Also, after being banished, Kent comes back in disguise, which is usually an element of comedies. For the true tragedy, the audience does not need to suspend disbelief, but the verisimilitude of Kent’s disguise is questionable. This feature points towards the morality play.
One of the most obvious ways that this tragedy derives material from the morality play is the plethora of vice characters—Edmund, Goneril, Regan, Oswald, and Cornwall. These characters all have a similar viewpoint on life and nature, which is modeled on that of the vice character’s. Edmund states this worldview: “Thou, Nature, art my goddess; to thy law/My services are bound. Wherefore should I/Stand in the plague of custom and permit/The curiosity of nations to deprive me” (Act 1, Scene 2, Lines 1-4). He, like the rest of the vice characters, believes that people who want something can have it as long as they have the ability to take it. Specifically for Edmund, the rules of legitimacy are manmade rather than natural. It means nothing if Edmund can be clever and strong enough to take his father’s land by cunning manipulation and force.