A Rebbe gives a child homework to review the Gemarah he has learned today.The father does not feel it to be necessary, and therefore signs that he did his Homework when he didn't. Is this outright lying or is it lying at all?
Why not you say? Chazal say "מותר לשנות מפני השלום". Meaning when Avraham does not need to know that Sara said that he is old, as this is something which Sara has to deal with herself, Hashem not only skips it but "edits "Sara's words as well.That tells us that what that person needs to know is 'his' truth.
Well, the Rebbe is at our service {for pay of course}.It is our call to have him do that which we are asking him to do.If a group pays a Rebbe to learn Gemara with the boys then this what he ought to do, although in his opinion Mishnayos would be way more beneficial and might turn them into much greater Talmidai Chachamim.
So too in our case then, although we can not affect the entire class with our way, but when all the difference is in his child then it is his call to have him brought up this way.
In the other hand we may claim that he is making light the respect for the Rebbe's way, which will somehow be felt by the Rebbe thus making it his business as well and would once again fall into the category of Sheker.
Now, the Rebbe is giving a prize to all who did their Homework, which brings in an issue of perhaps being Genaiva as the Rebbe is not obligated to give this prize and is giving it for following his way rather than the father's way?.
As an addition, We find in Masechet Kalla Rabbosi Perek 4 Halacha 22' that it allows and encourages at times when it is my concern only, for someone to answer one's curiosity with a simple "I don't know" although he does know. Which shows us that where it is not something I am expected to share with you I can just say "I don't know".
So can you define "The Truth" in this in this matter?