having the right to say; being in a position to criticize
Fixed expression used almost exclusively in negative or rhetorical contexts to mean someone is not in a position to say something, often because they are guilty of the same thing. Common patterns: 言えた義理ではない, 言えた義理か, 言えた義理じゃない.
I know I'm not really in a position to say this to you, but I wish you had come a little earlier.
You were late yourself, so you have no right to tell others to be punctual.
Formed from 言えた, the potential past form of 言う, and 義理 in the sense of grounds or standing; it commonly occurs in negative expressions denying someone the standing to criticize.