This poem operates at the intersection of ethics and emotion. You can’t discuss the moral lessons of the poem without discussing what emotions are found in it.
In the first stanza, the narrator describes two instances in which he’s angry. In the first, he’s angry with a friend and expresses that anger, and it passes. In the second, he’s angry with an enemy, and he does not express it. The anger doesn’t pass, but instead increases. This is a lesson about emotion, but it spills into morality: how you handle your relationships and emotions determines what you feel later. More simply, when you communicate about your anger, you can let it go.
The later stanzas describe the narrator tending his anger like a garden (or at least a poison tree in a garden). As he tends his anger, feeding it with fear, it grows. It appears to be a healthy fruit, but it isn’t. This has more lessons on emotion: fear and anger are linked.
In the final stanza, the enemy eats the poison fruit and dies. The emotional lesson here is clear: anger is deadly. Taken together, lessons can be drawn.
Be careful how you treat your anger.
Anger can appear attractive on the surface.
Anger is ultimately deadly.
The explicitly moral lesson is "don’t feed your anger."
William Blake intends, in A Poison Tree, to warn his readers that if they ignore his message regarding the "deceitful wiles" that cause hatred to intensify due to a lack of communication, they too can end up "outstretch'd beneath the tree" or be a person destroyed by his own "wrath." In the poem, the narrator's "foe" becomes less afraid of the narrator, and does not realize the depth of his hatred as the narrator "sunned it with smiles" misleading the enemy. The deceit becomes so intense that it bears "an apple bright." Most readers would be familiar with any story of the core or center of an apple being bad, as it appears in The Creation, when Eve first eats from the apple and then deceives Adam- the figurative "poison" being how they lost their innocence and Eve effectively poisoned Adam's mind and also in Snow White, the wicked queen deceives Snow White, also an innocent young girl literally poisoned.
The moral lessons in A Poison Tree include the need to be cautious of the motives of others and the ability of others to manipulate the innocent. Furthermore, the reader should recognize evil within himself before it becomes destructive and he is "glad" to see his enemy dead, even though he lured him to his death. The reader should ensure open communication and should not nurture hatred or "wrath" or it will "grow."