Crush almonds into smaller pieces with a mortar and pestle or with a rolling pin.
Spread almonds in a single layer in a large skillet over high heat. Add corn syrup; cook, stirring gently to prevent almonds from clumping together, until corn syrup coats almonds, 2 to 3 minutes. Spread almonds on the prepared baking sheet. Cool until hardened and set.
Toss lettuce, blackberries, and feta cheese together in a large bowl.
Pour lemon juice into a small bowl. Drizzle in olive oil, whisking constantly until blended into the lemon juice. Whisk sesame oil into the dressing.
Break up cooled almonds and add to the salad. Mix dressing into the salad.