In a large skillet, heat 1 tablespoon of the oil until shimmering. Add the turnips and radishes and cook over moderately high heat, stirring, until lightly browned and crisp-tender, 10 minutes.
Add the honey and cook over moderate heat, stirring, until the vegetables are glazed, 5 minutes. Add the soy sauce and cook until syrupy, 5 minutes longer.
Add the lemon juice and the Swiss chard; cook until the chard is wilted, 2 minutes. Raise the heat to high and cook until all of the liquid has evaporated, 2 minutes longer; keep warm.