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on (one's) way
In the process of traveling to or leaving some place. We were a little late leaving the house, but we're on our way! I just want to get a drink of water, and then I'll be on my way.
*on one's way (to some place)
leaving one place for another; en route to a place. (*Typically: be ~; get ~.) I have to leave. I am on my way to the bank. I will be there soon. I'm on my way now.
on one's way
(to something or some place) Go to on the way (to something or some place).