Of course if I could definitively answer your question here I would be a very rich man, as this is still an incredibly contested event. That being said, we can make a few assertions.

The 'freemasons' you refer to are P2. This was a secret and illegal lodge in Italy, something akin to a covert government, comprised of incredibly influential people from public life. The master of the lodge was Licio Gelli, a powerful banker. The lodge drew membership from many politicians (including future prime minister Silvio Berlusconi), media magnates (including the operators of national papers and television stations), the military (including generals and the secret service) and the former Italian royal family.

This secret society was uncovered as two large criminal operations fell apart during the late 1970s and early 1980s. The first was the Banco Ambrosiano scandal. This was a bank, operated by Roberto Calvi, which had the Vatican Bank as its biggest customer. Calvi and his bank were almost certainly laundering and funneling huge amounts of illegal currency, both for the Italian mafia and for the Vatican and US to international concerns around the world. As the system disintegrated, it became dangerous to those who may be implicated, who David Yallop asserts were within the Vatican. Calvi fled to London but was found and murdered. The P2 lodge, who referred to themselves as the frati neri, hung his corpse under Blackfriars bridge; supposedly as some kind of warning.

The second involved Michele Sindona, a mafioso and the head of a corrupt banking outfit similarly tied up with Banco Ambrosiano. It is claimed that he was involved in making illegal payments directly to members of the Vatican, including Vatican Bank's head Archbishop Paul Marcinkus. Sidona, despite being in prison for murder, was also assassinated with cyanide in his coffee.

This VERY VERY condensed account is the foundation of Yallop's claim: that His Holiness John Paul I had been made aware of the financial crimes and 'freemason' penetration within the Vatican and was about to act. His murder was therefore to protect the perpetrators, as were the murders of Calvi, Sidona and several others.

The actual mechanics of murdering a pope are discussed in the book you mention and it is something you will have to read yourself if you want to draw a personal conclusion. Your friend isn't indulging in any 'conspiracy theories' in so far as the corruption, murders and secret societies of Italy at the time, which are now a matter of record. However, the direct link to John Paul I's death is subjective.

If you are going to read the book, please also read 'A Thief in the Night', which is the response of John Cornwall to Yallop's work.

Edit: I can't type/speak.