Hello,
If it has been written that "they can accept or deny the payment in the lieu of notice period, depending on the criticality of the assignment/ work as deemed fit", then chances are bleak that sending notice will be of any help to you.
However if you do not want any letter from them and you are ready to fight the case (in case they file) then go ahead and leave the company.
Generally companies do not file suit for breach of this employment condition.
Regards