"Having had my lunch, I will come back,"
you are putting yourself in the middle of the action; that is, now that you have had your lunch, you are ready to go back to your office or workplace (if that is the case in this instance). The phrase "I will come back" implies that you are addressing someone who is already there (perhaps on the phone with you or by text); otherwise, you would say, "Having had my lunch, I will now go back."
EDIT: You can put both in the future by saying,
"Once I have lunch, I will be back," or, "Once I have had lunch, I will come back,"
or, as you also correctly suggested,
"After having my lunch, I will come back."
So, to correct myself, "Having had my lunch" is not exactly equivalent to saying "After having my lunch/After having had my lunch" in your example.
Although this is outside the scope of your question regarding grammar and usage, a native English speaker in casual conversation with a co-worker might simply say,
"I'll be back after lunch. See you then." :-)