I don't remember ever asking if He ever lied. :/
No cognition to logic and reason? I don't remember that I asked you for permission. You asked about the early life of the Christ and possible actions without sinning. What is the most common form of SIN learned by a child?

"I didn't do that...................."

Deflection of personal responsibility via the transmission that is a LIE. Accordingly, there is no sin possible by a child that has yet to reach the age of reason/accountability. The reason there is no chronological history of the Christ until it is demonstrated that He reached this age of reason at the young age of 12. (Luke 2:39-52)
The scriptures simply point out that even through Jesus was God incarnate, the humanity within Him was tempted in every way as any human is tempted to sin. (Hebrews 4:15) Was Jesus tempted to sin........every day of His life while on earth.
He prayed until His sweat turned to blood in order to combat this human temptation to sin. (Luke 22:40-44). Thus, Jesus was a babe, a child, an adolescent, and an adult.......just as every human that was ever born, and tempted to sin every day of His life, yet sinned not. Jesus was lacking no trait that is exampled in humanity......He wept (John 11:35), He rejoiced (Luke 10:21), He mourned (John 11:35), He suffered, the Cross..............finally, He died and proclaimed "......it is finished" (John 19:30). What was finished, His mission as a Human in becoming the perfect sacrificial lamb without spot nor blemish.....the only human to ever walk this life of humanity and SIN NOT. It is finished is referring to the fact His, birth, life, death and resurrection was the fulfillment to the Letter of the Old Law, ending it at the cross. (Matt. 5:17-19) Making way for a New Testament of Grace (a new covenant between man and God as prophesied in Jer. 31:31-34).