Is it morally permissible for a lay Catholic to minister a non-Catholic wedding?
It depends upon the circumstances in the situation at hand. Is this a religious ceremony at a non-Catholic church and the lay Catholic is being asked to serve as a non-Catholic Christian minister? In such a case, no. A Catholic layman cannot act as a minister in a non-Catholic Christan church.
However, perhaps you have in mind a lay Catholic presiding in a civil capacity at a non-Catholic wedding (e.g., judge, justice of the peace). So long as he is qualified by the state to preside at a civil ceremony and so long as there is no obvious impediment to the marriage (e.g., previous marriage, close blood relationship), yes, a Catholic layman could perform this civil function for the state.