“留下来吃饭”常见的英文表达有：
Stay for dinner.
这是最简洁、常用的说法，适用于各种较为随意、日常的场景，比如朋友来家里做客，快到饭点时主人这么说。例如：Don't rush off. Stay for dinner.（别急着走，留下来吃饭。）
Stay and have dinner with us.
这种表达更显热情、诚恳，强调希望对方能留下一起用餐，常用于想要特别款待客人或者关系比较亲密的人。例如：It's getting late. Stay and have dinner with us.（天色不早了，留下来和我们一起吃饭吧。）
Why don't you stay and eat with us?
这是以提出建议的方式邀请对方留下吃饭，语气比较温和、委婉，给对方留有一定的选择空间。例如：You've helped a lot today. Why don't you stay and eat with us?（你今天帮了不少忙，留下来和我们一起吃饭吧？）