Combine the garlic, anchovies, and lemon zest and juice in a food processor and process until it forms a smooth paste, scraping down the sides as needed. Transfer to a small pan and warm over low heat, stirring, about 2 minutes, then slowly whisk in the olive oil until smooth. Keep warm.

In a serving bowl, toss the lettuces and radishes with 3 tablespoons of the dressing. Add a few grinds of pepper. Pour the remaining dressing into a small pitcher or bowl. Serve the salad with the crisps and the extra dressing.