Izuku had you on his lap after his mother asked him to take care of the child of one of his mother's friends, in which this friend was a single mother and had no one else to take care of the child.

He accepted even though he knew it was risky, he always spent time training and worried that at some point he would accidentally hurt you.

For now you were on his lap while he combed your hair gently so as not to hurt you.