I have my lunch.这句话是不对的.不过在有些语境下也可以使用.比如
同学问你：
Do you want to go for lunch together?
你回答说：
I have my lunch.意思就是你带了午饭了.
I have had = I have done
I have done something 相信你也懂了吧 就是我完成了什么事
我已经吃过午饭了 I have had my lunch.
However,我基本没听人这么说过.一般会用在对话中起到强调的作用.
比如大家在讨论一本书,你说
I have read the book.
就是你已经读过这本书了,强调这个已经完成的状态.