About the use of future tense

I am not having lunch tomorrow, unless I'm really hungry.

Is the correct answer. Present tense in the second sentence, because it's obvious you are not talking about the present, because you already know whether you are hungry now or not.

Also, try swapping them and you'll see it right away:

Unless I'm really hungry, I am not having lunch tomorrow.

With the similar:

If I'm not really hungry, I am not having lunch tomorrow.

You would never say either of those:

Unless I will be really hungry, I am not having a lunch tomorrow.
If I won't be really hungry, I am not having lunch tomorrow.

Another examples to prove that present tense really expresses future condition:

If I don't get the money, I'll be really angry.
If you fail the school exam, I won't give you your allowance!

Neither of OP's suggestions are correct. Nor does @RiMMER's answer improve things by inserting the word a.

There are probably several better ways to phrase the statement, one of which is

I will not [or won't] have lunch tomorrow unless I get really hungry.

I'm not sure exactly how to explain what's wrong with the alternatives, but it's to do with using I am (present tense) when talking about something in the future. This is fine if that future is unquestionably expected to take place. But in this case the rest of the sentence casts serious doubt on whether it will in fact come to pass. It's inappropriate to use the present tense here because it implies that at the time of speaking the future being talked about is fully expected to arrive in due course.