Not much difference, but a little. "Did you have lunch today?" would imply that the opportunity to have lunch has now passed. If you didn't have lunch, then you've missed it. It is something that a friend or relative might say to someone if they are worried that the person is not eating enough. "Have you had lunch today?" is asking for the same information, but assumes that it might still be possible to have lunch today. It is something that I might ask someone if I am about to have a late lunch and I am inviting them to join me if they haven't already had lunch.

i think you would be fine using either one. you might also consider these options. Did you eat lunch today? Have you eaten lunch today?

Past simple (did have) is usually used to talk about some action that happened in the past and has no connection to the present or future. It can also be a reference to the fact that the action happened once at a particular time in the past and is completely over now. For example, here the lunch was scheduled at a particular time and the question is whether you went there or skipped it. Present perfect (have had) has a connection to the present/future, it suggests that there was no specific time for lunch, or day's schedule is not over yet and there's still a chance to go and have lunch later. And it also suggests repetitiveness of this action, for example, you work at the office and go to lunch daily.