Lutheran Claimants for the Papacy were people claiming they should be on the throne of the Papacy instead of the current Pope, following the original Lutherans' fight for what Martin Luther originally didn't want in the form of making him the Pope.
Martin VI (1522 - 1526)
Martin Luther only became the anti-Pope by the will of other German peasants. They stormed his church and carried him out against his will, already excommunicated, the claim to the throne wasn't that big of a deal. Adrian VI and Pius IV, however, hated him and Pius was only too happy to make sure he would be burned at the stake in 1526.
Sixtus V (1526 - 1533)
Carl Pfaff became the spiritual leader of the Lutherans after Luther's death and he claimed himself to be Luther's rightful successor and named himself Sixtus V. However, he lost many of his followers who tried to leave as fast as they could, he later supported the Hungarian part of the Protestant Wars, only to be killed by a hooded assassin in 1533.
Martin VII (1533 - 1539)
Mark Unger, a right hand of Sixtus took over afterward as Martin VII and tried to base himself in Scotland while the regency of Robert IV of Scotland underway. He tried to secretly turns the king to his fate, only to be banished at the order of the Scottish lords, he escaped by ship to America and their ship landed in what in OTL became Quebec. He named the river (St. Martin's river) and created a settlement called the New Rome. He also supported the Hungarian Protestant Wars.
Papal Lutheran Claimant
Clement VII (1539 - 1547)
David Ross became the claimant, but most of the population already converted back to Catholic or created their own church without the Pope and Clement's papacy was soon encircled by other Scottish settlements and Clement had to pay Robert IV for keeping his land. Gregory XIII asked king Gustav I of Sweden to talk with him and tried to reunite Christians. The new Pope Innocent IX was even more diplomatic, but Clement died before any talk could go throw.
Pius IV (1547 - 1549)
Jakob Danielsen was a member of a Lutheran family which settled in Sweden, where they went after Martin Luther was burned at the stake and they used the fact that Gustav I was Lutheran. He sailed to the New Rome in 1546 claiming he had a divine revelation that he should be the Pope, the people welcomed him as they saw Clement as a danger due to his friendly relations with the Popes. The first thing the new Pope did was naming himself Pius, thus saying that Pius IV was really a pretender and made a letter in which he insulted Innocent IX and all non-Lutherans. His reign was marked by a Scottish invasion of the Papacy, this cost him his life, but people from the city crushed the army, which Robert thought was big enough (but it wasn't). Robert and Innocent said that all they wanted was really to unite.
Peter II (1549 - 1553)
Peter Pfaff was a nephew of Sixtus V and became a spiritual leader of the Lutherans after the invasion, he said he would be willing to join up with Innocent IX, under the condition that he would become they both be Popes, when Innocent read this, his already weak heart couldn't take this insult. Gustav I quickly paid the Cardinals to push a non-fanatic on the throne (as he was afraid of a holy war against him). Alexander VIII was a student of Innocent and liked his ideas and, in fact, in 1553 he said yes to what Peter wanted, but all he got was another insult, Peter II had just died and another fanatic took the Lutheran Papacy. This time it was too much, Alexander declared a Crusade.
Sixtus VI (1553 - 1555)
James Shannon was made a successor by Peter himself and claimed to be the only true Pope. Soon he was, however, under all swords of attack by the Spanish and Scots and in 1555 he was murdered.
Paul III (1555 - 1567)
A monk called Joseph and a few others who believed in his divine authority fled New Rome and went to settle in Iceland, Christian III never acknowledged them and slowly the world forgot about them. In 1567 his favorite became the next Pope.
Peter III (1567 - 1573)
After Paul's death the group fell apart and the last person to claim being the leader of Lutherans was a monk called Robert. He died of an illness and officially ended the claimant line.