The couple's troubles began after they started an appeal on fundraising website Kickstarter last month to help finance the cabin, which will sleep five and cost an estimated £90,000 to build at their campsite, West Stow Pods, near Bury St Edmunds in Suffolk.
Soon after launching the bid for investors, they received a flurry of legal threats from the Tolkien Estate, along with Middle Earth Enterprises - which owns worldwide rights to the works - and Warner Brothers, which produced the Hollywood movies based on the books.
Mr Lengyel, 53, said: "The Tolkien Estate has asked us not to use 'Poddit Hole', which is absolutely ridiculous. We have got to call the project something, what would they like us to call it? Even though we have bent over backwards to meet their demands they are still wanting more."
Warner Brothers and Middle Earth Enterprises also contacted the Kickstarter website to have the couple's appeal removed - losing them £2,000 in donations.
The appeal, which is still titled Poddit Hole, has now been reinstated with all references to the films and books removed. So far it has raised £18,000.
Last week Mr Lengyel and his wife, also 53, received a legal document from the Tolkien solicitors, Maier Blackburn, rejecting their attempt to license the project or pay for the rights. It claimed the Lengyels are trying to use Tolkien's work for commercial gain.
Mr Lengyel said: "We are not trying to damage their brand or do anything offensive and there's a lot of local and national interest in the project."
Steven Maier, of Maier Blackburn, refused to comment on the dispute but confirmed the Tolkien Estate had contacted West Stow Pods.
He said: "I can also confirm that the Tolkien Estate has not licensed the use of intellectual property in the works of JRR Tolkien in connection with this or any similar venture."
- Daily Mail