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To make the dip: In a food processor, pulse the cream cheese and salmon until combined, 5 to 7 pulses.
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Add the remaining dip ingredients and pulse until combined and the dip is your desired consistency. Transfer to a bowl.
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Refrigerate, covered, for at least 1 hour and up to 24 hours to let the flavors meld. The dip will thicken as it chills. Taste and add more salt, pepper, and/or lemon juice as needed.
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To make the chips: Preheat the oven to 350°F with a rack in the middle. Line a baking sheet with parchment.
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Using a serrated knife, slice the bagels in half, top to bottom, to make half-moons. Slice each half-moon into approximately 1/8"-thick rounds.
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Transfer the bagel slices to a medium bowl, drizzle with the olive oil, and toss to coat.
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Arrange the slices in a tightly packed layer (a little overlap is OK) on the prepared baking sheet. Sprinkle with the flaky salt.
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Bake for 20 to 25 minutes, until golden brown and crisp. Let the bagel chips cool completely on the baking sheet.
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Just before serving, garnish the dip with additional chopped dill. Serve with the bagel chips alongside.
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Storage information: Store bagels chips in an airtight container at room temperature for 3 to 4 weeks. Freeze for longer storage. Store dip, covered, in the refrigerator, for up to 2 days.
