What's the difference between
I'm going to eat my lunch
I have to go for my lunch
and where can I use these sentences?
The first sentence says that you are about to eat your lunch; it may or may not imply that you are leaving the present location to do so, depending on the context.
The second says that it is time for you to eat lunch and that you will be leaving the present location to do so. You would say this when leaving the office to go to the canteen or deli, for example. 'I have to' implies that it is necessary for you to do so, perhaps because you have a set lunch hour.