In a medium saucepan, combine cranberries, lemon zest, juice from ½ lemon, and sugar, and place over medium heat.
Simmer until cranberries begin to pop (use a spatula to slightly crush cranberries as needed) and sauce thickens, about 10 minutes.
Remove from heat and allow to cool to room temperature.
Transfer cooled cranberry mixture to a food processor along with chickpeas, juice from remaining ½ lemon, and 1 teaspoon honey. Season with salt and pepper and pulse until incorporated. With motor running, slowly stream in olive oil and process until smooth, scraping down sides of bowl as necessary. Taste for seasoning and adjust as desired.
Cover and refrigerate until ready to serve.