Gothic was the language of the Goths; the oldest known Germanic language, it is now extinct and left no descendants.
Gothic was the first language that J.R.R. Tolkien studied for his own pleasure, and it may have given an impulsion in the first development of Qenya. Tolkien even attempted to reconstruct some parts of the language and such elements survived in his conlang Taliska. He also composed a poem, Bagme Bloma "The Flower of the Trees"
Since Old English in Lord of the Rings represents Rohirric, Tolkien used Gothic to represent the language of their ancestors, the Northmen of Rhovanion; as mentioned, Gothic had no descendants, so Old English is not directly related to it, and therefore it does not reflect that between Northern and Rohirric.