Will Allah answer my prayer for my son to succeed in his studies, even though I lied to my colleagues about his academic results to cover up family matters and protect my children?

There is no sin upon you for not mentioning your son's failure in mathematics during the Tawjihi, and there is no harm in a person concealing something about themselves or their child. As for your informing [people] of his success before the mathematics [result] was finalized, what is permissible in this regard is to use allusive language that does not amount to a lie, because "in allusive speech there is room to avoid lying." One must avoid lying unless there is an urgent necessity. Strive to teach your children and expose yourselves to Allah's blessings by supplicating during times when prayers are answered, and repent from sins, for they are a cause of deprivation.