Is it permissible to pray for the forgiveness of the deceased who did not pray, and is adopting the views that permit this considered following dispensations, or is there flexibility in the matter?

It is permissible to supplicate for the deceased and ask for forgiveness and mercy for him if his father did not deny the obligatory nature of prayer and was not an infidel. This is supported by several statements:

The majority of jurists believe that one who abandons prayer out of laziness, while acknowledging its obligatory nature, does not commit an act of disbelief that expels him from the fold of Islam.

Some of those who assert the disbelief of one who abandons prayer stipulate that a specific individual is only declared a disbeliever after being called to prayer and refusing. If the clear evidence (hujjah) has not been established against him, he is not considered a disbeliever. Thus, he would have died a Muslim, and it is recommended to seek forgiveness for him.

Even according to the view that one who abandons prayer out of laziness is a disbeliever, he might have an excuse, making conditional supplication for him permissible.

It is narrated from Sheikh Ibn Uthaymeen that it is permissible to make a conditional supplication, such as saying: "O Allah, if my son is known to You as a Muslim, then forgive him and have mercy on him."