I am an artist who has been told they are infringing on a copyright by a company, however my work differs significantly from the original.

There are several issues here that you raise, and no one can give you an opinion unless they see your work and the Lionsgate work to compare them. First, the myth that there is certain "percentage" of a work that can be used without infringing needs to be put to rest. The only way you can use someone else's copyrighted work without permission is if your use is a "fair use." Fair use is a judgment made on a number of factors, and at the end of the day only a court's opinion counts. Second, you mention "derivative work." If your work is based on a pre-existing work, then it is a derivative work and infringes the copyright of the underlying work if you did not get permission to make your work. The third issue you raise is whether your work is an infringement at all. Again, this is a judgment call. You do not have to make an identical copy to infringe a copyrighted work - you only need to make a "substantial copy." Either Lionsgate believes that your work is infringing, or else they are trying to bully you. If you choose to fight them, you should get professional assistance.