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."