There’s two points to be made here: The first concerning your question about your son; the second concerning your response to his sin.
First, it is absolutely correct that it is a serious matter for a child to deliberately lie to his parents, and a child should confess such a sin to a priest when he is able to go to confession the next time. Your son’s book was correct that God forgives us as soon as we repent. Ordinarily, we still must go to sacramental confession before receiving Communion when the sin we repent is a mortal sin, but when there is no opportunity for confession, a perfect act of contrition suffices (with the assumption that the person will go to confession as soon as it is possible to do so).
It could be argued that your son had no opportunity to go to confession before he received Communion, and so his act of contrition could suffice (so long as he also goes to confession at the next opportunity). So, while your son should still go to confession for his sin of lying, only he could make the determination in conscience if he was unable to go to confession and if he had made a perfect act of contrition. In short, I don’t think your son acted wrongly, but he could be encouraged next time to consider if waiting a day or two for Communion—depending on when he next attended Mass after confession—is a hardship sufficient to outweigh the ordinary protocol of going first to confession.
Second, while parents have a duty to form their children in the faith, they should take care not to do anything that may put their children at risk for scrupulosity. There is nothing wrong with reminding your son to consider the fact that he lied to his parents during his next examination of conscience, and with helping him to discern whether or not it constituted a mortal sin. But I hesitate at the point of telling a 10-year-old child that he cannot receive Communion at Mass because he has no opportunity for confession before that Mass.
In the first place, his inability to go to confession before Mass is not his fault. A child’s opportunities to approach confession on his own are more limited than an adult’s. Secondly, depending on the seriousness of the lie and the child’s level of knowledge and consent, he may not have committed a mortal sin. And, finally, I believe that even parents should not take it upon themselves to do anything that gives the implication that they control their children’s consciences (either by telling them they cannot receive the sacraments or by asking them questions that put them in a position of having to explain their sacramental prudential judgments—as happened when you asked your son about the Mass at which you had told him he couldn’t receive Communion).
Perhaps as a way of resolving this “disagreement,” you might propose to your son that you and he both do some research together on the sacraments of confession and the Eucharist.