All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is no disagreement among the scholars of Islam (may Allah's Mercy be upon them) that the flesh of the pigs (lard, lean and any other parts of pig) is completely forbidden. Indeed, Allah has specifically mentioned lean meat since it is the most wanted and beneficial part of a lawful animal. However, all parts of the pig are impure and forbidden.
As for the verse that mentions the prohibition of animal fat, it is:
{And to those who are Jews We prohibited every animal of uncloven hoof; and of the cattle and the sheep We prohibited to them their fat, except what adheres to their backs or the entrails or what is joined with bone. [By] that We repaid them for their injustice. And indeed, We are truthful.} [Quran 6: 146]
This verse informs of the Divine prohibition of fats unto Jews as a punishment to them due to their transgression and objection to their Messengers.
As for Muslims, it is lawful to eat the flesh (lard and lean meat) of each and every animal whose meat is lawful for us to eat.
Allah knows best.