All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Your grandmother is blameless for favoring her young son over her mother with food because she favored a baby who is weaker and more in need of food. Indeed, a child is different from an old person who is able to bear hunger and look for food. Nevertheless, she is guilty of lying. She was required to be truthful with her mother and tell her that she had only a morsel for her son.
We hope that Allaah The Almighty will forgive her because she showed regret and sadness because of this, and this a form of repentance. Ibn Mas‘ood narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Regret is repentance.” [Ibn Maajah, Al-Haakim and Ahmad]
‘Aa’ishah narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said to her: “If you commit a sin, ask Allaah for forgiveness; because repentance is to regret [the sin] and ask Allaah for forgiveness.” [Al-Bayhaqi]
Your grandmother should ask Allaah The Almighty to forgive her and she should intensify supplication in favor of her mother, as this is a form of dutifulness to her. Her mother is now dead and a deceased person’s need for supplication is greater than his need for food and drink during his lifetime.
Allaah Knows best.