I would say concerning Ephesians 6:1, that the best way to interpret the phrase is to compare it to the instructions given to wives and to slaves, since all three groups (children, wives and slaves) represent those who have a subordinate function in society. The instructions are similar enough that some sort of similar idea is most likely present when it comes to how one connects to the Lord. In Ephesians 5:22 (and 24, by implication), wives are told to submit to their husbands “as to the Lord.” The notion of means is not present, but motivation is: submit to one’s husband as you would to the Lord because the husband is the conduit of Christ’s love, whether he knows it or not!
In Ephesians 6:5 and 7, slaves are told to obey their masters “as to the Lord.” Both the wording and the notion are similar to what wives are to do. In Ephesians 6:1 “in the Lord” is the expression. One would be hard-pressed to single out children so as to make their instructions materially different from that given to wives AND slaves (this contrasts with the verb used for wives [submit] as opposed to the one used for children and slaves [obey], for wives can be singled out for a different kind of treatment, since their relationship symbolizes the relationship of the church to Christ).
Though grammatically, the idea of EN + dative could be means, this does not seem to work well in Ephesians 6:1. The idea that children should obey their parents only when the parents’ instructions and wishes are in the Lord’s will is both off the wall and impossible in the context. To argue that children—and children alone of these three subordinate groups—should discern what the Lord’s will is when it comes to obedience is illogical and unbiblical. A better alternative to either of these is this: children obey your parents because of the Lord. The causal notion of EN + dative is frequently used by Paul, it fits well with the motivation phrases for wives and slaves, and is eminently satisfactory in the context. I take it that this is the right interpretation of this verse. Thanks for the interaction.