Place the apricots in a lidded dish, cover with cold water, put the lid on, and soak overnight.
Place the apricots and water in a medium-sized saucepan, stir in the honey, and bring to a boil.
Add the coconut milk and lemon juice. Stir constantly, mashing the apricots as they begin to soften, until the liquid has reduced and you have a thick, pulpy pudding.
Portion into serving dishes. This can be served hot or refrigerated until cold.