Place the coconut milk and the cream cheese in a large bowl. Mix with an immersion blender or hand mixer until smooth.
Add the maple syrup, vanilla extract, and chia seeds and whisk or blend well.
Cover the bowl and refrigerator for at least 4 hours, or overnight.
Whisk the pudding mixture every 30 minutes for the first 2 hours to help break up the thick chia and cream cheese and distribute the seeds throughout the pudding. Whisk again thoroughly before serving.
Place the strawberries, granulated sugar, and lemon juice in a medium saucepan over medium heat.
Stir frequently until juices form and begin to boil.
Turn the heat to low and cook for 10 minutes, stirring occasionally. Remove from heat and cool slightly.
Blend the sauce until smooth.
Whisk the chia pudding mixture thoroughly. Add about ¼ cup into 4 serving dishes.
Spoon 1 tablespoon of strawberry sauce onto the pudding.
Divide the remaining chia pudding evenly among the serving dishes. Top with another tablespoon or so of the pureed strawberries. Sprinkle graham cracker pieces on top, then serve.