do you want to have a lunch with me today.Is this correct

征求对方同意要用could 和would的委婉句式,
lunch/supper/breakfast前面不加冠词a,固定句式：have lunch/supper/breakfast,但没有have a lunch这种说法,只有have a dinner
正确句型：would you like have luch with me today?
或者could you have lunch with me today?
或者will you please have lunch with me today?

would you like to have a lunch with me today

incorrect!
do you want to have lunch with me today?

应该是“would you like to have launch with me today?"
回答如果是愿意可以说”I‘d like to "
如果不愿意则是“ I am afriad i can't