I have eaten lunch at 1 pm
could be used to describe ones habits. For example:
Q: Do you eve eat lunch as late as 12:30?
A: I have eaten lunch at 1 pm,
But aside from this somewhat unlikely example, I can't think of a context in which this sentence would be likely. The usual way to indicate when you ate lunch today, or on another specified day, would be to use the simple past. For example:
- I ate lunch at 1:00 pm.
- On Thursday I ate lunch at 1:00 pm.
A sentence such as
I had eaten lunch at 1 pm.
would normally be used only when a subsequnt action is described. For example:
I had eaten lunch at 1 pm. Just as I was finished, the telephone rang.
Even this would be more likely to be expressed using the simple past:
That day, I ate lunch at 1 pm. Just as I was finished, the telephone rang.