This is not a direct scripture referred by Pillai Lokacharya. He was referring to a legend famous in Tamil Nadu about a Nayanar named Siru Tondar.
Once Lord Shiva wanted to test his devotion and went to his home in a disguise as a mendicant where he has asked Nayanar's son as food. This is not related to yajnas.
At once, Siruthondar ran to the temple and fell at the feet of the Vairavar and invited him to the house for bhiksha (food). The Vairavar, however, hesitated and remarked, "I doubt whether you will be able to fulfill the exacting conditions I shall demand for accepting your Bhiksha — so, better leave me alone."
Siruthondar was greatly grieved. He had thought that this mendicant had been specially sent by God to enable him to adhere to his vow and feed a Siva bhakta every day. He was prepared to meet any demand from the Siva bhakta, if only he agreed to take the Bhiksha.
The mendicant then revealed his condition, "Oh devotee, it is my habit to eat once in six months the fresh meat of a Pasu. That time has now come. I doubt whether you will satisfy me."
This word Pasu has two meanings: an animal and a human being. Siruthondar thought that the mendicant only meant animal meat and readily agreed! To his surprise, however, the mendicant revealed that meant human flesh! He also added, "Oh friend, it should be the meat of a child. The child should be five years of age. He must be healthy. He should be the only son of his parents. Such a boy must be held by the mother and cut into pieces by his father. This meat must be cooked nicely and offered to me."
Without the least hesitation, Siruthondar accepted conditions and took the mendicant home.
"How to find a boy of the mendicant's description?" Siruthondar thought.
He then realized that his own son fitted the description. The noble wife agreed, too, and asked Siruthondar to get the child from school. As soon as he came, the mother held him on her lap. The innocent child was laughing when Siruthondar, with one stroke cut his throat.
The head is generally unfit for cooking, and is not fit for being offered to the Lord. So, they gave it away to the maid-servant and began to cook, the rest of the meat. After worshipping the mendicant, Siruthondar was preparing to offer him Bhiksha. The mendicant ascertained the method adopted by them in cooking the meat and Siruthondar Nayanar explained everything (except the fact that it was their own son that they had sacrificed).
The mendicant said he would eat the head, too. The maid-servant had anticipated this and had the head cooked and ready.
Once again, Siruthondar requested the Yogi to have his meal. Now, the Yogi wanted another Siva bhakta to eat with him. There was no one except the Siruthondar Nayanar himself. So, he sat with the Yogi, ready to eat the flesh of his son, to please the Yogi.
Yet, one more condition had to be fulfilled! The Yogi said that unless the host's son ate with him, the Yogi would not eat!
Now, the second condition is host's son should eat the food also. But the son was already dead. But the Yogi asked him to call and said he would appear.
Now, Nayanar goes into the kitchen and calls his son loudly. Surprisingly the son came out from the kitchen. They felt happy that their son is alive and asked him to dine along with the Yogi. When they came out, there was neither Yogi nor the meat served to the yogi who is none other than Shiva himself.
Later, it was revealed to Nayanar and his wife that it was a leela and he took the couple to his abode.
Part of this answer is quoted from Skandha Gurunatha Page. I do not hold copy rights. Complete story is found in their webpage.
This is not guesswork. This is based on the writing style of Pillai Lokacharya and translation of Prapanna Paritrana by Alkondavilli Govindachacharya Swami, a renowned Vaishnava scholar.