Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfics might combine the noble and brooding nature of Jon Snow with the epic fantasy world of Lord of the Rings in interesting ways, like having him be a lost traveler in Middle - earth or having some sort of magical connection between the two universes.
A very popular Jon Snow fanfiction is 'Jon Snow: The True Heir'. It plays on the idea of his true parentage and how that could change the power dynamics in the Game of Thrones realm. In this fanfic, he has to fight for his rightful place. Another one is 'Jon Snow's Unseen Path' which shows his journey through some less - explored aspects of the story. 'Jon Snow and the Alliance' is also quite good, where he forms unexpected alliances to survive the cutthroat Game of Thrones politics.
One common theme is the idea of an outsider. Jon Snow was an outsider in Westeros, and in Lord of the Rings fanfiction, he could be an outsider in Middle - earth as well. Another theme could be the battle against great evil, just like he fought the White Walkers in his own world, he could be fighting Sauron in Middle - earth.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.
The North would surely support him. They have always seen him as one of their own and a great leader. Also, the wildlings might back him, considering he has a history of working with them and understanding their plight. Davos Seaworth would most likely be on his side as well, given his loyalty to Jon in the past.
Daenerys Targaryen is often paired with Jon Snow in these fanfictions. Their connection in the original series, along with their both being strong leaders, makes for an interesting dynamic. They could rule Westeros together in a new era of peace and prosperity after Jon's rebirth.