Place a steamer basket into a multi-functional pressure cooker (such as Instant Pot). Add potatoes to the basket, then lay broccolini on top. Pour 1 1/2 cups water over the vegetables. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 3 minutes. Allow 5 to 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer broccolini and potatoes to a serving bowl and let cool.
Meanwhile, whisk olive oil, lemon juice, garlic, oregano, salt, and pepper together in a small bowl. Pour dressing over broccolini and potatoes. Serve immediately or cover and refrigerate, removing from the refrigerator 1 hour before serving.