Combine shallot, vinegar, and salt in a medium bowl and let stand 10 minutes to soften and lightly pickle shallot. Meanwhile, thinly slice lemon with a handheld slicer, removing seeds; stack, cut in half, then cut into very small triangles.
Stir lemon, parsley, and capers into bowl with shallot mixture. Add oil and stir to combine. Let stand 30 minutes.
Make ahead: Up to 5 days, chilled airtight (color will fade).