Combine blackberries, maple syrup, and lemon juice in a medium saucepan over medium heat. Cook, stirring occasionally, until berries break down and release their juices, about 5 minutes. The mixture should look jammy but still have some whole berries.

Transfer half the compote to a fine-mesh sieve set over a bowl. Press firmly with a spoon to extract a smooth seedless puree; discard seeds. Stir this puree back into the remaining chunky compote for a silky-yet-textured swirl. Let cool completely, about 20 minutes.

In a large bowl, whisk together almond milk, coconut milk, chia seeds, maple syrup, vanilla, and salt until no clumps remain. Let sit 5 minutes, then whisk again vigorously to prevent seeds from clumping at the bottom.

Divide half the chia mixture among four 8-oz jars. Dollop 1 heaping tablespoon of cooled blackberry compote into each jar and swirl gently with a chopstick or knife. Top with remaining chia mixture. Cover and refrigerate at least 4 hours, preferably overnight, until thickened to a pudding consistency.

Stir each pudding before serving to reincorporate any separated liquid. Top with remaining blackberry compote, fresh blackberries, and toasted almonds if using. The puddings keep covered in the refrigerator for up to 5 days.